From rote@zedat.fu-berlin.de Fri Jan 07 16:26:35 2022 Received: from outpost1.zedat.fu-berlin.de ([130.133.4.66]) by list1.zedat.fu-berlin.de (Exim 4.94) for facets-of-complexity@lists.fu-berlin.de with esmtps (TLS1.2) tls TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384 (envelope-from ) id 1n5r8U-0012Uh-MP; Fri, 07 Jan 2022 16:26:34 +0100 Received: from inpost2.zedat.fu-berlin.de ([130.133.4.69]) by outpost.zedat.fu-berlin.de (Exim 4.94) for facets-of-complexity@lists.fu-berlin.de with esmtps (TLS1.2) tls TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384 (envelope-from ) id 1n5r8U-002Zza-Je; Fri, 07 Jan 2022 16:26:34 +0100 Received: from strecke.imp.fu-berlin.de ([160.45.40.209]) by inpost2.zedat.fu-berlin.de (Exim 4.94) for facets-of-complexity@lists.fu-berlin.de with esmtpsa (TLS1.2) tls TLS_ECDHE_RSA_WITH_AES_128_GCM_SHA256 (envelope-from ) id 1n5r8U-002mf8-Ef; Fri, 07 Jan 2022 16:26:34 +0100 Message-ID: Date: Fri, 7 Jan 2022 16:26:34 +0100 MIME-Version: 1.0 User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:91.0) Gecko/20100101 Thunderbird/91.4.1 From: =?UTF-8?Q?G=c3=bcnter_Rote?= To: facets-of-complexity@lists.fu-berlin.de References: <147fe76c-7f8c-0aea-94df-3ea570a624f5@inf.fu-berlin.de> Content-Language: en-US In-Reply-To: <147fe76c-7f8c-0aea-94df-3ea570a624f5@inf.fu-berlin.de> Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit X-Original-Sender: rote@inf.fu-berlin.de X-Originating-IP: 160.45.40.209 X-purgate: clean X-purgate-type: clean X-purgate-ID: 151147::1641569194-0009FB93-80D288D3/0/0 X-Bogosity: Ham, tests=bogofilter, spamicity=0.167864, version=1.2.4 X-Spam-Flag: NO X-Spam-Status: No, score=-50.0 required=5.0 tests=ALL_TRUSTED X-Spam-Checker-Version: SpamAssassin 3.4.6 on Tuvalu.ZEDAT.FU-Berlin.DE X-Spam-Level: Subject: [Facets-of-complexity] Invitation to Monday Lecture - Jan 10 2022, 2:15 p.m., online via zoom X-BeenThere: facets-of-complexity@lists.fu-berlin.de X-Mailman-Version: 2.1.29 Precedence: list List-Id: announcements of Monday lectures and other events List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-List-Received-Date: Fri, 07 Jan 2022 15:26:35 -0000 Invitation link: https://tu-berlin.zoom.us/j/69716124232?pwd=dzFlcTFHMmFXRTE5QmZLaEV5N0FRUT09 Time: Monday, Jan 10, 2022 - 14:15 h Lecture: Vera Traub (ETH Zürich): Better-Than-2 Approximations for Weighted Tree Augmentation The Weighted Tree Augmentation Problem (WTAP) is one of the most basic connectivity augmentation problems. It asks how to increase the edge-connectivity of a given graph from 1 to 2 in the cheapest possible way by adding some additional edges from a given set. There are many standard techniques that lead to a 2-approximation for WTAP, but despite much progress on special cases, the factor 2 remained unbeaten for several decades. In this talk we present two algorithms for WTAP that improve on the longstanding approximation ratio of 2. The first algorithm is a relative greedy algorithm, which starts with a simple, though weak, solution and iteratively replaces parts of this starting solution by stronger components. This algorithm achieves an approximation ratio of (1 + ln 2 + ε) < 1.7. Second, we present a local search algorithm that achieves an approximation ratio of 1.5 + ε (for any constant ε > 0). This is joint work with Rico Zenklusen. ===== There will be no colloquium on this Monday. From itabrunke@zedat.fu-berlin.de Wed Jan 12 18:03:37 2022 Received: from outpost1.zedat.fu-berlin.de ([130.133.4.66]) by list1.zedat.fu-berlin.de (Exim 4.94) for facets-of-complexity@lists.fu-berlin.de with esmtps (TLS1.2) tls TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384 (envelope-from ) id 1n7h28-001hzQ-Tv; Wed, 12 Jan 2022 18:03:37 +0100 Received: from inpost2.zedat.fu-berlin.de ([130.133.4.69]) by outpost.zedat.fu-berlin.de (Exim 4.94) with esmtps (TLS1.2) tls TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384 (envelope-from ) id 1n7h28-0047vA-QT; Wed, 12 Jan 2022 18:03:36 +0100 Received: from ip5f5af673.dynamic.kabel-deutschland.de ([95.90.246.115] helo=[192.168.0.2]) by inpost2.zedat.fu-berlin.de (Exim 4.94) with esmtpsa (TLS1.2) tls TLS_ECDHE_RSA_WITH_AES_128_GCM_SHA256 (envelope-from ) id 1n7h28-000NdJ-F7; Wed, 12 Jan 2022 18:03:36 +0100 From: "I.Brunke" To: facets-of-complexity@lists.fu-berlin.de Message-ID: Date: Wed, 12 Jan 2022 18:03:36 +0100 User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:68.0) Gecko/20100101 Firefox/68.0 SeaMonkey/2.53.10.1 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="------------59902AFFCF5977DBDD90F08C" X-Antivirus: Avast (VPS 220112-2, 12.1.2022), Outbound message X-Antivirus-Status: Clean X-Original-Sender: i.brunke@fu-berlin.de X-Originating-IP: 95.90.246.115 X-ZEDAT-Hint: A X-purgate: clean X-purgate-type: clean X-purgate-ID: 151147::1642007016-00086027-91307092/0/0 X-Bogosity: Ham, tests=bogofilter, spamicity=0.034948, version=1.2.4 X-Spam-Flag: NO X-Spam-Status: No, score=-50.0 required=5.0 tests=ALL_TRUSTED,HTML_MESSAGE, T_REMOTE_IMAGE X-Spam-Checker-Version: SpamAssassin 3.4.6 on Vanuatu.ZEDAT.FU-Berlin.DE X-Spam-Level: Subject: [Facets-of-complexity] Invitation to Monday's Lecture & Colloquium Jan.17 - online via Zoom. X-BeenThere: facets-of-complexity@lists.fu-berlin.de X-Mailman-Version: 2.1.29 Precedence: list List-Id: announcements of Monday lectures and other events List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-List-Received-Date: Wed, 12 Jan 2022 17:03:37 -0000 This is a multi-part message in MIME format. --------------59902AFFCF5977DBDD90F08C Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Dear all, next Monday's Lecture and Colloquium will take place *online via Zoom* on January 17.* Please find link to Zoom Meeting here: ** **https://tu-berlin.zoom.us/j/69716124232?pwd=dzFlcTFHMmFXRTE5QmZLaEV5N0FRUT09 * *A password is not required!** *** *You all are cordially invited!* *_Location_**: ** * *Online via Zoom.* *_Monday's Lecture_: María A. Hernández Cifre (Universitdad de Murcia)* *_Time_: **Monday, January 17 - 14:15 h* *_Title_: On discrete Brunn-Minkowski type inequalities* *_Abstract_:* The classical Brunn-Minkowski inequality in the n-dimensional Euclidean space asserts that the volume (Lebesgue measure) to the power 1/n is a concave functional when dealing with convex bodies (non-empty compact convex sets). This result has become not only a cornerstone of the Brunn-Minkowski theory, but also a powerful tool in other related fields of mathematics. In this talk we will make a brief walk on this inequality, as well as on its extensions to the Lp-setting, for non-negative values of p. Then, we will move to the discrete world, either considering the integer lattice endowed with the cardinality, or working with the lattice point enumerator, which provides with the number of integer points contained in a given convex body: we will discuss and show certain discrete analogues of the above mentioned Brunn-Minkowski type inequalities in both cases. This is about joint works with Eduardo Lucas and Jesús Yepes Nicolás. *Break* *_Monday's Colloquium_: Ji Hoon Chun (Technische Universität Berlin)* *_Time_: **Monday, January 17**- 16:00 h s.t.* *_Title_: The Sausage Conjecture in dimension 4* *_Abstract_:* The Sausage Catastrophe (Jörg Wills) is the observation that in d = 3 and d = 4, the densest packing of n spheres is a sausage for small n and jumps to a full-dimensional packing for large n without passing through any intermediate dimensions. We denote the smallest value of n for which the densest packing is full-dimensional by k_d. We discuss some upper and lower bounds for k_3 and k_4, including k_3 ≤ 56 by Wills (1985) and k_4 < 375,769 by Gandini and Zucco (1992). We present some initial improvements to the upper bound for k_4 via extending the work of Gandini and Zucco. *You all are cordially invited!* -- -- Diese E-Mail wurde von Avast Antivirus-Software auf Viren geprüft. https://www.avast.com/antivirus --------------59902AFFCF5977DBDD90F08C Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: 8bit Dear all,

next Monday's Lecture and Colloquium will take place online via Zoom on January 17.

Please find link to Zoom Meeting here:

https://tu-berlin.zoom.us/j/69716124232?pwd=dzFlcTFHMmFXRTE5QmZLaEV5N0FRUT09

A password is not required!
You all are cordially invited!

Location:

Online via Zoom.


Monday's Lecture: María A. Hernández Cifre (Universitdad de Murcia)

Time: Monday, January 17 - 14:15 h

Title: On discrete Brunn-Minkowski type inequalities

Abstract:

The classical Brunn-Minkowski inequality in the n-dimensional Euclidean space asserts that the volume (Lebesgue measure) to the power 1/n is a concave functional when dealing with convex bodies (non-empty compact convex sets). This result has become not only a cornerstone of the Brunn-Minkowski theory, but also a powerful tool in other related fields of mathematics.
In this talk we will make a brief walk on this inequality, as well as on its extensions to the Lp-setting, for non-negative values of p. Then, we will move to the discrete world, either considering the integer lattice endowed with the cardinality, or working with the lattice point enumerator, which provides with the number of integer points contained in a given convex body: we will discuss and show certain discrete analogues of the above mentioned Brunn-Minkowski type inequalities in both cases.
This is about joint works with Eduardo Lucas and Jesús Yepes Nicolás.


Break

Monday's Colloquium: Ji Hoon Chun (Technische Universität Berlin)

Time: Monday, January 17 - 16:00 h s.t.

Title: The Sausage Conjecture in dimension 4

Abstract:

The Sausage Catastrophe (Jörg Wills) is the observation that in d = 3 and d = 4, the densest packing of n spheres is a sausage for small n and jumps to a full-dimensional packing for large n without passing through any intermediate dimensions. We denote the smallest value of n for which the densest packing is full-dimensional by k_d. We discuss some upper and lower bounds for k_3 and k_4, including k_3 ≤ 56 by Wills (1985) and k_4 < 375,769 by Gandini and Zucco (1992). We present some initial improvements to the upper bound for k_4 via extending the work of Gandini and Zucco.

You all are cordially invited! 
--

Virenfrei. www.avast.com
--------------59902AFFCF5977DBDD90F08C-- From itabrunke@zedat.fu-berlin.de Wed Jan 12 20:19:45 2022 Received: from outpost1.zedat.fu-berlin.de ([130.133.4.66]) by list1.zedat.fu-berlin.de (Exim 4.94) for facets-of-complexity@lists.fu-berlin.de with esmtps (TLS1.2) tls TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384 (envelope-from ) id 1n7j9p-001tRp-RR; Wed, 12 Jan 2022 20:19:42 +0100 Received: from inpost2.zedat.fu-berlin.de ([130.133.4.69]) by outpost.zedat.fu-berlin.de (Exim 4.94) with esmtps (TLS1.2) tls TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384 (envelope-from ) id 1n7j9p-000eAe-Nr; Wed, 12 Jan 2022 20:19:41 +0100 Received: from ip5f5af673.dynamic.kabel-deutschland.de ([95.90.246.115] helo=[192.168.0.2]) by inpost2.zedat.fu-berlin.de (Exim 4.94) with esmtpsa (TLS1.2) tls TLS_ECDHE_RSA_WITH_AES_128_GCM_SHA256 (envelope-from ) id 1n7j9p-000cUJ-CI; Wed, 12 Jan 2022 20:19:41 +0100 From: "I.Brunke" To: facets-of-complexity@lists.fu-berlin.de Message-ID: <77828c69-4280-1c18-e234-b9edc266a4fa@fu-berlin.de> Date: Wed, 12 Jan 2022 20:19:40 +0100 User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:68.0) Gecko/20100101 Firefox/68.0 SeaMonkey/2.53.10.1 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="------------DDF8389FDBE11A37B741CB4E" X-Antivirus: Avast (VPS 220112-2, 12.1.2022), Outbound message X-Antivirus-Status: Clean X-Original-Sender: i.brunke@fu-berlin.de X-Originating-IP: 95.90.246.115 X-ZEDAT-Hint: A X-purgate: clean X-purgate-type: clean X-purgate-ID: 151147::1642015181-0003D58E-B11FE71A/0/0 X-Bogosity: Ham, tests=bogofilter, spamicity=0.050686, version=1.2.4 X-Spam-Flag: NO X-Spam-Status: No, score=-50.0 required=5.0 tests=ALL_TRUSTED,HTML_MESSAGE, T_REMOTE_IMAGE X-Spam-Checker-Version: SpamAssassin 3.4.6 on Tokelau.ZEDAT.FU-Berlin.DE X-Spam-Level: Subject: [Facets-of-complexity] Korrektur Title Coll.: Invitation to Monday's Lecture & Colloquium Jan.17. X-BeenThere: facets-of-complexity@lists.fu-berlin.de X-Mailman-Version: 2.1.29 Precedence: list List-Id: announcements of Monday lectures and other events List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-List-Received-Date: Wed, 12 Jan 2022 19:19:46 -0000 This is a multi-part message in MIME format. --------------DDF8389FDBE11A37B741CB4E Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Dear all, next Monday's Lecture and Colloquium will take place *online via Zoom* on January 17.* Please find link to Zoom Meeting here: ** **https://tu-berlin.zoom.us/j/69716124232?pwd=dzFlcTFHMmFXRTE5QmZLaEV5N0FRUT09 * *A password is not required!** *** *You all are cordially invited!* *_Location_**: ** * *Online via Zoom.* *_Monday's Lecture_: María A. Hernández Cifre (Universitdad de Murcia)* *_Time_: **Monday, January 17 - 14:15 h* *_Title_: On discrete Brunn-Minkowski type inequalities* *_Abstract_:* The classical Brunn-Minkowski inequality in the n-dimensional Euclidean space asserts that the volume (Lebesgue measure) to the power 1/n is a concave functional when dealing with convex bodies (non-empty compact convex sets). This result has become not only a cornerstone of the Brunn-Minkowski theory, but also a powerful tool in other related fields of mathematics. In this talk we will make a brief walk on this inequality, as well as on its extensions to the Lp-setting, for non-negative values of p. Then, we will move to the discrete world, either considering the integer lattice endowed with the cardinality, or working with the lattice point enumerator, which provides with the number of integer points contained in a given convex body: we will discuss and show certain discrete analogues of the above mentioned Brunn-Minkowski type inequalities in both cases. This is about joint works with Eduardo Lucas and Jesús Yepes Nicolás. *Break* *_Monday's Colloquium_: Ji Hoon Chun (Technische Universität Berlin)* *_Time_: **Monday, January 17**- 16:00 h s.t.* *_Title_: The Sausage Catastrophe **in dimension 4* *_Abstract_:* The Sausage Catastrophe (Jörg Wills) is the observation that in d = 3 and d = 4, the densest packing of n spheres is a sausage for small n and jumps to a full-dimensional packing for large n without passing through any intermediate dimensions. We denote the smallest value of n for which the densest packing is full-dimensional by k_d. We discuss some upper and lower bounds for k_3 and k_4, including k_3 ≤ 56 by Wills (1985) and k_4 < 375,769 by Gandini and Zucco (1992). We present some initial improvements to the upper bound for k_4 via extending the work of Gandini and Zucco. *You all are cordially invited!* -- -- Diese E-Mail wurde von Avast Antivirus-Software auf Viren geprüft. https://www.avast.com/antivirus --------------DDF8389FDBE11A37B741CB4E Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: 8bit Dear all,

next Monday's Lecture and Colloquium will take place online via Zoom on January 17.

Please find link to Zoom Meeting here:

https://tu-berlin.zoom.us/j/69716124232?pwd=dzFlcTFHMmFXRTE5QmZLaEV5N0FRUT09

A password is not required!
You all are cordially invited!

Location:

Online via Zoom.


Monday's Lecture: María A. Hernández Cifre (Universitdad de Murcia)

Time: Monday, January 17 - 14:15 h

Title: On discrete Brunn-Minkowski type inequalities

Abstract:

The classical Brunn-Minkowski inequality in the n-dimensional Euclidean space asserts that the volume (Lebesgue measure) to the power 1/n is a concave functional when dealing with convex bodies (non-empty compact convex sets). This result has become not only a cornerstone of the Brunn-Minkowski theory, but also a powerful tool in other related fields of mathematics.
In this talk we will make a brief walk on this inequality, as well as on its extensions to the Lp-setting, for non-negative values of p. Then, we will move to the discrete world, either considering the integer lattice endowed with the cardinality, or working with the lattice point enumerator, which provides with the number of integer points contained in a given convex body: we will discuss and show certain discrete analogues of the above mentioned Brunn-Minkowski type inequalities in both cases.
This is about joint works with Eduardo Lucas and Jesús Yepes Nicolás.


Break

Monday's Colloquium: Ji Hoon Chun (Technische Universität Berlin)

Time: Monday, January 17 - 16:00 h s.t.

Title: The Sausage Catastrophe in dimension 4

Abstract:

The Sausage Catastrophe (Jörg Wills) is the observation that in d = 3 and d = 4, the densest packing of n spheres is a sausage for small n and jumps to a full-dimensional packing for large n without passing through any intermediate dimensions. We denote the smallest value of n for which the densest packing is full-dimensional by k_d. We discuss some upper and lower bounds for k_3 and k_4, including k_3 ≤ 56 by Wills (1985) and k_4 < 375,769 by Gandini and Zucco (1992). We present some initial improvements to the upper bound for k_4 via extending the work of Gandini and Zucco.

You all are cordially invited! 
--

Virenfrei. www.avast.com
--------------DDF8389FDBE11A37B741CB4E-- From itabrunke@zedat.fu-berlin.de Wed Jan 19 18:26:59 2022 Received: from outpost1.zedat.fu-berlin.de ([130.133.4.66]) by list1.zedat.fu-berlin.de (Exim 4.94) for facets-of-complexity@lists.fu-berlin.de with esmtps (TLS1.2) tls TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384 (envelope-from ) id 1nAEja-002WT5-Pm; Wed, 19 Jan 2022 18:26:58 +0100 Received: from inpost2.zedat.fu-berlin.de ([130.133.4.69]) by outpost.zedat.fu-berlin.de (Exim 4.94) for facets-of-complexity@lists.fu-berlin.de with esmtps (TLS1.2) tls TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384 (envelope-from ) id 1nAEja-002r65-Mc; Wed, 19 Jan 2022 18:26:58 +0100 Received: from ip5f5af450.dynamic.kabel-deutschland.de ([95.90.244.80] helo=[192.168.0.2]) by inpost2.zedat.fu-berlin.de (Exim 4.94) for facets-of-complexity@lists.fu-berlin.de with esmtpsa (TLS1.2) tls TLS_ECDHE_RSA_WITH_AES_128_GCM_SHA256 (envelope-from ) id 1nAEja-001RFp-CV; Wed, 19 Jan 2022 18:26:58 +0100 From: "I.Brunke" To: facets-of-complexity@lists.fu-berlin.de Message-ID: Date: Wed, 19 Jan 2022 18:26:57 +0100 User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:68.0) Gecko/20100101 Firefox/68.0 SeaMonkey/2.53.10.2 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="------------326CB802BCCAE5BA804DFB96" X-Antivirus: Avast (VPS 220119-4, 19.1.2022), Outbound message X-Antivirus-Status: Clean X-Original-Sender: i.brunke@fu-berlin.de X-Originating-IP: 95.90.244.80 X-ZEDAT-Hint: A X-purgate: clean X-purgate-type: clean X-purgate-ID: 151147::1642613218-0006CA84-51AC9EA9/0/0 X-Bogosity: Ham, tests=bogofilter, spamicity=0.036759, version=1.2.4 X-Spam-Flag: NO X-Spam-Status: No, score=-50.0 required=5.0 tests=ALL_TRUSTED, HTML_IMAGE_ONLY_32,HTML_MESSAGE,T_REMOTE_IMAGE X-Spam-Checker-Version: SpamAssassin 3.4.6 on Palau.ZEDAT.FU-Berlin.DE X-Spam-Level: Subject: [Facets-of-complexity] Invitation to Monday's Lecture Jan.24 - online via Zoom. X-BeenThere: facets-of-complexity@lists.fu-berlin.de X-Mailman-Version: 2.1.29 Precedence: list List-Id: announcements of Monday lectures and other events List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-List-Received-Date: Wed, 19 Jan 2022 17:26:59 -0000 This is a multi-part message in MIME format. --------------326CB802BCCAE5BA804DFB96 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Dear all, next Monday's Lecture will take place *online via Zoom* on January 24.* Please find link to Zoom Meeting here: ** **https://tu-berlin.zoom.us/j/69716124232?pwd=dzFlcTFHMmFXRTE5QmZLaEV5N0FRUT09 * A password is *not* required! *You all are cordially invited!* *_Location_**: ** * *Online via Zoom.* *_Monday's Lecture_: Günter Rote (Freie Universität Berlin)* *_Time_: **Monday, January 24 - 14:15 h* *_Title_: The maximum number of minimal dominating sets in a tree* *_Abstract_:* A tree with n vertices has at most 95^n/13 minimal dominating sets. The growth constant λ=^13 √95≈1.4194908 is best possible. It is obtained in a semi-automatic way as a kind of "/dominant eigenvalue/" of a bilinear operation on sextuples that is derived from the dynamic-programming recursion for computing the number of minimal dominating sets of a tree. The core of the method tries to enclose a set of sextuples in a six-dimensional geometric body with certain properties, which depend on some putative value of λ. This technique is generalizable to other counting problems, and it raises interesting questions about the "growth" of a general bilinear operation. We also derive an output-sensitive algorithm for listing all minimal dominating sets with linear set-up time and linear delay between successive solutions. *You all are cordially invited!* -- Diese E-Mail wurde von Avast Antivirus-Software auf Viren geprüft. https://www.avast.com/antivirus --------------326CB802BCCAE5BA804DFB96 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: 8bit Dear all,

next Monday's Lecture will take place online via Zoom on January 24.

Please find link to Zoom Meeting here:

https://tu-berlin.zoom.us/j/69716124232?pwd=dzFlcTFHMmFXRTE5QmZLaEV5N0FRUT09

A password is not required!

You all are cordially invited!

Location:

Online via Zoom.

Monday's Lecture: Günter Rote (Freie Universität Berlin)

Time: Monday, January 24 - 14:15 h

Title: The maximum number of minimal dominating sets in a tree

Abstract:

A tree with n vertices has at most 95n/13 minimal dominating sets. The growth constant λ=13√95≈1.4194908 is best possible. It is obtained in a semi-automatic way as a kind of "dominant eigenvalue" of a bilinear operation on sextuples that is derived from the dynamic-programming recursion for computing the number of minimal dominating sets of a tree. The core of the method tries to enclose a set of sextuples in a six-dimensional geometric body with certain properties, which depend on some putative value of λ. This technique is generalizable to other counting problems, and it raises interesting questions about the "growth" of a general bilinear operation.

We also derive an output-sensitive algorithm for listing all minimal dominating sets with linear set-up time and linear delay between successive solutions.


You all are cordially invited!


Virenfrei. www.avast.com
--------------326CB802BCCAE5BA804DFB96-- From itabrunke@zedat.fu-berlin.de Wed Jan 26 16:03:50 2022 Received: from outpost1.zedat.fu-berlin.de ([130.133.4.66]) by list1.zedat.fu-berlin.de (Exim 4.94) for facets-of-complexity@lists.fu-berlin.de with esmtps (TLS1.2) tls TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384 (envelope-from ) id 1nCjpu-003jed-60; Wed, 26 Jan 2022 16:03:50 +0100 Received: from inpost2.zedat.fu-berlin.de ([130.133.4.69]) by outpost.zedat.fu-berlin.de (Exim 4.94) with esmtps (TLS1.2) tls TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384 (envelope-from ) id 1nCjpt-002VVc-FT; Wed, 26 Jan 2022 16:03:49 +0100 Received: from [95.90.243.185] (helo=[192.168.0.2]) by inpost2.zedat.fu-berlin.de (Exim 4.94) with esmtpsa (TLS1.2) tls TLS_ECDHE_RSA_WITH_AES_128_GCM_SHA256 (envelope-from ) id 1nCjpt-003Yyt-54; Wed, 26 Jan 2022 16:03:49 +0100 From: "I.Brunke" To: facets-of-complexity@lists.fu-berlin.de Message-ID: Date: Wed, 26 Jan 2022 16:03:48 +0100 User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:68.0) Gecko/20100101 Firefox/68.0 SeaMonkey/2.53.10.2 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="------------03D02541362135FF76D80A2C" X-Antivirus: Avast (VPS 220126-4, 26.1.2022), Outbound message X-Antivirus-Status: Clean X-Original-Sender: i.brunke@fu-berlin.de X-Originating-IP: 95.90.243.185 X-ZEDAT-Hint: A X-purgate: clean X-purgate-type: clean X-purgate-ID: 151147::1643209430-00086027-8EE10F99/0/0 X-Bogosity: Ham, tests=bogofilter, spamicity=0.000000, version=1.2.4 X-Spam-Flag: NO X-Spam-Status: No, score=-50.0 required=5.0 tests=ALL_TRUSTED,HTML_MESSAGE, T_REMOTE_IMAGE X-Spam-Checker-Version: SpamAssassin 3.4.6 on Palau.ZEDAT.FU-Berlin.DE X-Spam-Level: Subject: [Facets-of-complexity] Invitation to Monday's Lecture & Colloquium Jan.31 - online via Zoom. X-BeenThere: facets-of-complexity@lists.fu-berlin.de X-Mailman-Version: 2.1.29 Precedence: list List-Id: announcements of Monday lectures and other events List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-List-Received-Date: Wed, 26 Jan 2022 15:03:50 -0000 This is a multi-part message in MIME format. --------------03D02541362135FF76D80A2C Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Dear all, next Monday's Lecture and Colloquium will take place *online via Zoom* on January 31.* Please find link to Zoom Meeting here: ** **https://tu-berlin.zoom.us/j/69716124232?pwd=dzFlcTFHMmFXRTE5QmZLaEV5N0FRUT09 * A password is not required!* *** *You all are cordially invited!* *_Location_**: ** * *Online via Zoom.* *_Monday's Lecture_: George Mertzios (Durham University)* *_Time_: **Monday, January 31 - 14:15 h* *_Title_: Algorithmic Problems on Temporal Graphs* *_Abstract_:* A temporal graph is a graph whose edge set changes over a sequence of discrete time steps. This can be viewed as a discrete sequence G_1, G_2, ... of static graphs, each with a fixed vertex set V. Research in this area is motivated by the fact that many modern systems are highly dynamic and relations (edges) between objects (vertices) vary with time. Although static graphs have been extensively studied for decades from an algorithmic point of view, we are still far from having a concrete set of structural and algorithmic principles for temporal graphs. Many notions and algorithms from the static case can be naturally transferred in a meaningful way to their temporal counterpart, while in other cases new approaches are needed to define the appropriate temporal notions. In particular, some problems become radically different, and often substantially more difficult, when the time dimension is additionally taken into account. In this talk we will discuss some natural but only recently introduced temporal problems and some algorithmic approaches to them. *Break* *_Monday's Colloquium_: Klaus Heeger (Technische Universität Berlin)* *_Time_: **Monday, January 31**- 16:00 h s.t.* *_Title_: Stable Matchings Beyond Stable Marriage* *_Abstract_:* Stable matchings are well-studied from computer science, mathematics, and economics. In the most basic setting, called Stable Marriage, there are two sets of agents. Each agent from one set has preferences over the agents from the other set. A matching assigns the agents into groups of two agents. A matching is called stable if there are no two agents preferring each other to the partners assigned to them. In this talk, we will review important parts of my forthcoming PhD thesis concerning the computational complexity of two extensions of this basic model: First, we assume that an instance of Stable Marriage is given, and the aim is to modify the instance (using as few "modifications" as possible) such that a given edge is part of some stable matching. Second, we assume that agents have preferences over sets of d-1 other agents (for some d>2). In this case, a matching matches agents into groups of size d, and a matching is stable if there are no d agents preferring to be matched together to being unmatched. While since 1991 this problem is known to be NP-complete, we study the case that the preferences of all agents are "similar". *You all are cordially invited!* -- -- Diese E-Mail wurde von Avast Antivirus-Software auf Viren geprüft. https://www.avast.com/antivirus --------------03D02541362135FF76D80A2C Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: 8bit Dear all,

next Monday's Lecture and Colloquium will take place online via Zoom on January 31.

Please find link to Zoom Meeting here:

https://tu-berlin.zoom.us/j/69716124232?pwd=dzFlcTFHMmFXRTE5QmZLaEV5N0FRUT09

A password is not required!
You all are cordially invited!

Location:

Online via Zoom.


Monday's Lecture: George Mertzios (Durham University)

Time: Monday, January 31 - 14:15 h

Title: Algorithmic Problems on Temporal Graphs

Abstract:

A temporal graph is a graph whose edge set changes over a sequence of discrete time steps. This can be viewed as a discrete sequence G_1, G_2, ... of static graphs, each with a fixed vertex set V. Research in this area is motivated by the fact that many modern systems are highly dynamic and relations (edges) between objects (vertices) vary with time. Although static graphs have been extensively studied for decades from an algorithmic point of view, we are still far from having a concrete set of structural and algorithmic principles for temporal graphs. Many notions and algorithms from the static case can be naturally transferred in a meaningful way to their temporal counterpart, while in other cases new approaches are needed to define the appropriate temporal notions. In particular, some problems become radically different, and often substantially more difficult, when the time dimension is additionally taken into account. In this talk we will discuss some natural but only recently introduced temporal problems and some algorithmic approaches to them.


Break

Monday's Colloquium: Klaus Heeger (Technische Universität Berlin)

Time: Monday, January 31 - 16:00 h s.t.

Title: Stable Matchings Beyond Stable Marriage

Abstract:

Stable matchings are well-studied from computer science, mathematics, and economics. In the most basic setting, called Stable Marriage, there are two sets of agents. Each agent from one set has preferences over the agents from the other set. A matching assigns the agents into groups of two agents. A matching is called stable if there are no two agents preferring each other to the partners assigned to them. In this talk, we will review important parts of my forthcoming PhD thesis concerning the computational complexity of two extensions of this basic model: First, we assume that an instance of Stable Marriage is given, and the aim is to modify the instance (using as few "modifications" as possible) such that a given edge is part of some stable matching. Second, we assume that agents have preferences over sets of d-1 other agents (for some d>2). In this case, a matching matches agents into groups of size d, and a matching is stable if there are no d agents preferring to be matched together to being unmatched. While since 1991 this problem is known to be NP-complete, we study the case that the preferences of all agents are "similar".

You all are cordially invited! 
--

Virenfrei. www.avast.com
--------------03D02541362135FF76D80A2C-- From itabrunke@zedat.fu-berlin.de Wed Feb 02 18:10:00 2022 Received: from outpost1.zedat.fu-berlin.de ([130.133.4.66]) by list1.zedat.fu-berlin.de (Exim 4.94) for facets-of-complexity@lists.fu-berlin.de with esmtps (TLS1.2) tls TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384 (envelope-from ) id 1nFJ8q-000BMa-4N; Wed, 02 Feb 2022 18:10:00 +0100 Received: from inpost2.zedat.fu-berlin.de ([130.133.4.69]) by outpost.zedat.fu-berlin.de (Exim 4.94) with esmtps (TLS1.2) tls TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384 (envelope-from ) id 1nFJ8p-000qWn-AB; Wed, 02 Feb 2022 18:09:59 +0100 Received: from ip5f5af673.dynamic.kabel-deutschland.de ([95.90.246.115] helo=[192.168.0.2]) by inpost2.zedat.fu-berlin.de (Exim 4.94) with esmtpsa (TLS1.2) tls TLS_ECDHE_RSA_WITH_AES_128_GCM_SHA256 (envelope-from ) id 1nFJ8p-000Kzm-18; Wed, 02 Feb 2022 18:09:59 +0100 From: "I.Brunke" To: facets-of-complexity@lists.fu-berlin.de, Neil Olver , Manuel Radons Message-ID: <63b682c2-fcb1-fea5-2a13-6c756f3f3a4b@fu-berlin.de> Date: Wed, 2 Feb 2022 18:09:58 +0100 User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:68.0) Gecko/20100101 Firefox/68.0 SeaMonkey/2.53.10.2 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="------------B5D5BF46D67DC54F118CC3FD" X-Antivirus: Avast (VPS 220202-0, 2.2.2022), Outbound message X-Antivirus-Status: Clean X-Original-Sender: i.brunke@fu-berlin.de X-Originating-IP: 95.90.246.115 X-ZEDAT-Hint: A X-purgate: clean X-purgate-type: clean X-purgate-ID: 151147::1643821800-00000547-D0E68B94/0/0 X-Bogosity: Ham, tests=bogofilter, spamicity=0.028035, version=1.2.4 X-Spam-Flag: NO X-Spam-Status: No, score=-50.0 required=5.0 tests=ALL_TRUSTED,HTML_MESSAGE, T_REMOTE_IMAGE,T_SCC_BODY_TEXT_LINE X-Spam-Checker-Version: SpamAssassin 3.4.6 on Palau.ZEDAT.FU-Berlin.DE X-Spam-Level: Subject: [Facets-of-complexity] Invitation to Monday's Lecture & Colloquium Feb.7 - online via Zoom. X-BeenThere: facets-of-complexity@lists.fu-berlin.de X-Mailman-Version: 2.1.29 Precedence: list List-Id: announcements of Monday lectures and other events List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-List-Received-Date: Wed, 02 Feb 2022 17:10:00 -0000 This is a multi-part message in MIME format. --------------B5D5BF46D67DC54F118CC3FD Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Dear all, next Monday's Lecture and Colloquium will take place *online via Zoom* on February 7.* Please find link to Zoom Meeting here: ** **https://tu-berlin.zoom.us/j/69716124232?pwd=dzFlcTFHMmFXRTE5QmZLaEV5N0FRUT09 * A password is not required!* *** *You all are cordially invited!* *_Location_**: ** * *Online via Zoom.* *_Monday's Lecture_: Neil Olver (London School of Economics and Political Science)* *_Time_: **Monday, February 7 - 14:15 h* *_Title_: Continuity, Uniqueness and Long-Term Behaviour of Nash Flows Over Time* *_Abstract_:* We consider a dynamic model of traffic that has received a lot of attention in the past few years. Users control infinitesimal flow particles aiming to travel from a source to destination as quickly as possible. Flow patterns vary over time, and congestion effects are modelled via queues, which form whenever the inflow into a link exceeds its capacity. We answer some rather basic questions about equilibria in this model: in particular /uniqueness/ (in an appropriate sense), and /continuity/: small perturbations to the instance or to the traffic situation at some moment cannot lead to wildly different equilibrium evolutions. To prove these results, we make a surprising connection to another question: whether, assuming constant inflow into the network at the source, do equilibria always eventually settle into a "steady state" where all queue delays change linearly forever more? Cominetti et al. proved this under an assumption that the inflow rate is not larger than the capacity of the network - eventually, queues remain constant forever. We resolve the more general question positively. (Joint work with Leon Sering and Laura Vargas Koch). *Break* *_Monday's Colloquium_: Manuel Radons (Technische Universität Berlin)* *_Time_: **Monday, February 7**- 16:00 h s.t.* *_Title_: Nearly flat polytopes in the context of Dürer's problem* *_Abstract_:* Dürer's problem asks whether every 3-polytope P has a net. Is there always a spanning tree T of its edge graph, so that if we cut P along T the resulting surface can be unfolded into the plane without self-overlaps? A common technique in recent works is to fix a spanning tree and then study the deformations of the corresponding unfolding induced by an affine stretching or flattening of P. In the first part of my talk I will highlight landmark results by Ghomi, O'Rourke and Tarasov that emanated from this approach. In the second part I will present my own work on the unfoldability of nested prismatoids, which follows a similar ansatz. *You all are cordially invited!* -- -- Diese E-Mail wurde von Avast Antivirus-Software auf Viren geprüft. https://www.avast.com/antivirus --------------B5D5BF46D67DC54F118CC3FD Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: 8bit Dear all,

next Monday's Lecture and Colloquium will take place online via Zoom on February 7.

Please find link to Zoom Meeting here:

https://tu-berlin.zoom.us/j/69716124232?pwd=dzFlcTFHMmFXRTE5QmZLaEV5N0FRUT09

A password is not required!
You all are cordially invited!

Location:

Online via Zoom.


Monday's Lecture: Neil Olver (London School of Economics and Political Science)

Time: Monday, February 7 - 14:15 h

Title: Continuity, Uniqueness and Long-Term Behaviour of Nash Flows Over Time

Abstract:

We consider a dynamic model of traffic that has received a lot of attention in the past few years. Users control infinitesimal flow particles aiming to travel from a source to destination as quickly as possible. Flow patterns vary over time, and congestion effects are modelled via queues, which form whenever the inflow into a link exceeds its capacity. We answer some rather basic questions about equilibria in this model: in particular uniqueness (in an appropriate sense), and continuity: small perturbations to the instance or to the traffic situation at some moment cannot lead to wildly different equilibrium evolutions.

To prove these results, we make a surprising connection to another question: whether, assuming constant inflow into the network at the source, do equilibria always eventually settle into a "steady state" where all queue delays change linearly forever more? Cominetti et al. proved this under an assumption that the inflow rate is not larger than the capacity of the network - eventually, queues remain constant forever. We resolve the more general question positively.

(Joint work with Leon Sering and Laura Vargas Koch).


Break

Monday's Colloquium: Manuel Radons (Technische Universität Berlin)

Time: Monday, February 7 - 16:00 h s.t.

Title: Nearly flat polytopes in the context of Dürer's problem

Abstract:

Dürer's problem asks whether every 3-polytope P has a net. Is there always a spanning tree T of its edge graph, so that if we cut P along T the resulting surface can be unfolded into the plane without self-overlaps? A common technique in recent works is to fix a spanning tree and then study the deformations of the corresponding unfolding induced by an affine stretching or flattening of P. In the first part of my talk I will highlight landmark results by Ghomi, O'Rourke and Tarasov that emanated from this approach. In the second part I will present my own work on the unfoldability of nested prismatoids, which follows a similar ansatz.

You all are cordially invited! 
--

Virenfrei. www.avast.com
--------------B5D5BF46D67DC54F118CC3FD-- From itabrunke@zedat.fu-berlin.de Tue Feb 08 16:58:35 2022 Received: from outpost1.zedat.fu-berlin.de ([130.133.4.66]) by list1.zedat.fu-berlin.de (Exim 4.94) for facets-of-complexity@lists.fu-berlin.de with esmtps (TLS1.2) tls TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384 (envelope-from ) id 1nHSsx-00457P-0N; Tue, 08 Feb 2022 16:58:31 +0100 Received: from inpost2.zedat.fu-berlin.de ([130.133.4.69]) by outpost.zedat.fu-berlin.de (Exim 4.94) for facets-of-complexity@lists.fu-berlin.de with esmtps (TLS1.2) tls TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384 (envelope-from ) id 1nHSsw-000LjI-Tx; Tue, 08 Feb 2022 16:58:30 +0100 Received: from [95.90.244.135] (helo=[192.168.0.2]) by inpost2.zedat.fu-berlin.de (Exim 4.94) for facets-of-complexity@lists.fu-berlin.de with esmtpsa (TLS1.2) tls TLS_ECDHE_RSA_WITH_AES_128_GCM_SHA256 (envelope-from ) id 1nHSsw-001WeG-JT; Tue, 08 Feb 2022 16:58:30 +0100 From: "I.Brunke" To: facets-of-complexity@lists.fu-berlin.de Message-ID: Date: Tue, 8 Feb 2022 16:58:30 +0100 User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:68.0) Gecko/20100101 Firefox/68.0 SeaMonkey/2.53.10.2 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="------------28DEB4948E24B457586F0BBC" X-Antivirus: Avast (VPS 220208-2, 8.2.2022), Outbound message X-Antivirus-Status: Clean X-Original-Sender: i.brunke@fu-berlin.de X-Originating-IP: 95.90.244.135 X-ZEDAT-Hint: A X-purgate: clean X-purgate-type: clean X-purgate-ID: 151147::1644335911-00000498-755A2A09/0/0 X-Bogosity: Ham, tests=bogofilter, spamicity=0.000570, version=1.2.4 X-Spam-Flag: NO X-Spam-Status: No, score=-50.0 required=5.0 tests=ALL_TRUSTED,HTML_MESSAGE, T_REMOTE_IMAGE,T_SCC_BODY_TEXT_LINE X-Spam-Checker-Version: SpamAssassin 3.4.6 on Niue.ZEDAT.FU-Berlin.DE X-Spam-Level: Subject: [Facets-of-complexity] Invitation to Monday's Lecture & Colloquium Feb.14 - online via Zoom. X-BeenThere: facets-of-complexity@lists.fu-berlin.de X-Mailman-Version: 2.1.29 Precedence: list List-Id: announcements of Monday lectures and other events List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-List-Received-Date: Tue, 08 Feb 2022 15:58:35 -0000 This is a multi-part message in MIME format. --------------28DEB4948E24B457586F0BBC Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Dear all, next Monday's Lecture and Colloquium will take place *online via Zoom* on February 14.* Please find link to Zoom Meeting here: ** **https://tu-berlin.zoom.us/j/69716124232?pwd=dzFlcTFHMmFXRTE5QmZLaEV5N0FRUT09 * A password is not required!* *** *You all are cordially invited!* *_Location_**: ** * *Online via Zoom.* *_Monday's Lecture_: Carlos Amendola (Technische Universität München)* *_Time_: **Monday, February 14 - 14:15 h* *_Title_: Estimating Gaussian mixtures using sparse polynomial moment systems* *_Abstract_:* The method of moments is a statistical technique for density estimation that solves a system of moment equations to estimate the parameters of an unknown distribution. A fundamental question critical to understanding identifiability asks how many moment equations are needed to get finitely many solutions and how many solutions there are. Since the moments of a mixture of Gaussians are polynomial expressions in the means, variances and mixture weights, one can address this question from the perspective of algebraic geometry. With the help of tools from polyhedral geometry, we answer this fundamental question for several classes of Gaussian mixture models. Furthermore, these results allow us to present an algorithm that performs parameter recovery and density estimation, applicable even in the high dimensional case. Based on joint work with Julia Lindberg and Jose Rodriguez (University of Wisconsin-Madison). *Break* *_Monday's Colloquium_: Marie Brandenburg (Max Planck Institut Leipzig)* *_Time_: **Monday, February 14**- 16:00 h s.t.* *_Title_: Intersection Bodies of Polytopes* *_Abstract_:* Intersection bodies are classical objects from convex geometry, that are constructed from given convex body. In the past, they have mainly been studied from the point of view of convex analysis. In this talk we investigate combinatorial and algebraic structures of intersection bodies of polytopes. We consider an algorithm to compute both the radial function and the algebraic boundary of these intersection bodies, and provide an upper bound for their degree. This is joint work with Katalin Berlow, Chiara Meroni and Isabelle Shankar. *You all are cordially invited!* -- -- Diese E-Mail wurde von Avast Antivirus-Software auf Viren geprüft. https://www.avast.com/antivirus --------------28DEB4948E24B457586F0BBC Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: 8bit Dear all,

next Monday's Lecture and Colloquium will take place online via Zoom on February 14.

Please find link to Zoom Meeting here:

https://tu-berlin.zoom.us/j/69716124232?pwd=dzFlcTFHMmFXRTE5QmZLaEV5N0FRUT09

A password is not required!
You all are cordially invited!

Location:

Online via Zoom.


Monday's Lecture: Carlos Amendola (Technische Universität München)

Time: Monday, February 14 - 14:15 h

Title: Estimating Gaussian mixtures using sparse polynomial moment systems

Abstract:

The method of moments is a statistical technique for density estimation that solves a system of moment equations to estimate the parameters of an unknown distribution. A fundamental question critical to understanding identifiability asks how many moment equations are needed to get finitely many solutions and how many solutions there are. 

Since the moments of a mixture of Gaussians are polynomial expressions in the means, variances and mixture weights, one can address this question from the perspective of algebraic geometry. With the help of tools from polyhedral geometry, we answer this fundamental question for several classes of Gaussian mixture models. Furthermore, these results allow us to present an algorithm that performs parameter recovery and density estimation, applicable even in the high dimensional case.

Based on joint work with Julia Lindberg and Jose Rodriguez (University of Wisconsin-Madison).


Break

Monday's Colloquium: Marie Brandenburg (Max Planck Institut Leipzig)

Time: Monday, February 14 - 16:00 h s.t.

Title: Intersection Bodies of Polytopes

Abstract:

Intersection bodies are classical objects from convex geometry, that are constructed from given convex body. In the past, they have mainly been studied from the point of view of convex analysis. In this talk we investigate combinatorial and algebraic structures of intersection bodies of polytopes. We consider an algorithm to compute both the radial function and the algebraic boundary of these intersection bodies, and provide an upper bound for their degree. This is joint work with Katalin Berlow, Chiara Meroni and Isabelle Shankar.

You all are cordially invited! 
--

Virenfrei. www.avast.com
--------------28DEB4948E24B457586F0BBC--