## Math Calendar

Monday, June 26, 2017

13:15-14:00

HFG 610

14:15-15:00

HFG 610

14:30-15:30

BBG 075

Master thesis presentation

Roeland Nusselder - Spike-based Long Short-Term Memory networks

see description

Abstract: Spiking neural networks are investigated both as biologically plausible models of neural computation and also as a potentially more efficient type of neural network. Recurrent neural networks, especially Long Short-Term Memory (LSTM) networks, have been central in state-of-the-art solutions for problems such as speech recognition and neural machine translation. Here, we design an analog gated Long Short-Term Memory (LSTM) cell where its constituent neurons can be substituted for efficient Adaptive Spiking Neurons (ASNs). For such ASNs, we derive the effective activation function.

We show how analog neurons with these activation functions can be used to create an analog LSTM cell, networks of these cells can then be trained with standard backpropagation. We train these LSTM networks on several supervised and reinforcement learning tasks that require the use of memory. Substituting the analog neurons for corresponding Adaptive Spiking Neurons, we then show that almost all resulting spiking neural network equivalents correctly compute the original tasks.

We show how analog neurons with these activation functions can be used to create an analog LSTM cell, networks of these cells can then be trained with standard backpropagation. We train these LSTM networks on several supervised and reinforcement learning tasks that require the use of memory. Substituting the analog neurons for corresponding Adaptive Spiking Neurons, we then show that almost all resulting spiking neural network equivalents correctly compute the original tasks.

15:15-16:15

BBG 017

Master thesis presentation

Dion Hartmann - Quantum intuitionistic logic and the Gelfand representation theorem

see description

Abstract:

The subject of this thesis is on the shared horizon of theoretical physics and logic: Quantum logic. In 1936, Birkhofff and von Neumann already formulated a quantum logic. But, this logic has some undesirable properties concerning the interpretation of the logical conjunction and disjunction as ``and'' and ``or''. Therefor, Landsman has recently set out to develop a new logic for quantum mechanics, which is set up inside a topos and thus is intuitionistic.

The construction of Landsmans intuitionistic quantum logic relies on the Gelfand representation theorem. However, to apply the theorem a constructive proof is needed. Coquand and Spitters recently published such a proof, but the material that was published is too condensed for our taste. So in this thesis we attempt to expand on this constructive proof of the Gelfand representation theorem and check all details the original authors left out. As a result, more insight is gained in the constructive proof of the Gelfand representation theorem, providing a stronger foundation for intuitionistic quantum logic.

The subject of this thesis is on the shared horizon of theoretical physics and logic: Quantum logic. In 1936, Birkhofff and von Neumann already formulated a quantum logic. But, this logic has some undesirable properties concerning the interpretation of the logical conjunction and disjunction as ``and'' and ``or''. Therefor, Landsman has recently set out to develop a new logic for quantum mechanics, which is set up inside a topos and thus is intuitionistic.

The construction of Landsmans intuitionistic quantum logic relies on the Gelfand representation theorem. However, to apply the theorem a constructive proof is needed. Coquand and Spitters recently published such a proof, but the material that was published is too condensed for our taste. So in this thesis we attempt to expand on this constructive proof of the Gelfand representation theorem and check all details the original authors left out. As a result, more insight is gained in the constructive proof of the Gelfand representation theorem, providing a stronger foundation for intuitionistic quantum logic.

Tuesday, June 27, 2017

13:15-14:15

HFG 610

Thursday, June 29, 2017

15:00-16:00

BBG 079

16:00-17:00

HFG 610

Abstract:

Mimetic methods aim to preserve structures/invariants of physical models or the differential equations in which these models are represented. One way of doing so is to write the model in terms of differential forms. The reduction operator or the De Rham map reduces differential forms to discrete degrees of freedom, the so-called cochains. The reduction operator commutes with the exterior derivative at the continuous level and the coboundary operator at the discrete level.

A reconstruction operator or Whitney map interpolates the cochains to differential forms. This reconstruction map should be constructed such that it commutes with the exterior derivative also.

These maps between a continuous description and a fully discrete description already allow one to preserve many invariants of physcal models.

In this presentation the main ideas will be presented for a general audience. Examples from fluid mechanics, solid mechanics and electromagnetism serve as an illustration of these ideas.

Mimetic methods aim to preserve structures/invariants of physical models or the differential equations in which these models are represented. One way of doing so is to write the model in terms of differential forms. The reduction operator or the De Rham map reduces differential forms to discrete degrees of freedom, the so-called cochains. The reduction operator commutes with the exterior derivative at the continuous level and the coboundary operator at the discrete level.

A reconstruction operator or Whitney map interpolates the cochains to differential forms. This reconstruction map should be constructed such that it commutes with the exterior derivative also.

These maps between a continuous description and a fully discrete description already allow one to preserve many invariants of physcal models.

In this presentation the main ideas will be presented for a general audience. Examples from fluid mechanics, solid mechanics and electromagnetism serve as an illustration of these ideas.

16:00-17:00

BBG 079

Friday, June 30, 2017

13:00-14:00

BBG 071

Master thesis presentation

Jan-Willem van Ittersum - Quantitative results on Diophantine equations in many variables

see description

Abstract:

A typical question in number theory is whether a given polynomial equation has integer solutions. We discuss a theorem of Birch who uses the so-called circle method to answer this question for polynomials in 'many' variables. In case there are integer solutions, we study the smallest integer solution. We present new upper bounds on this smallest integer solution, which are obtained using a quantitative version of the Nullstellensatz.

A typical question in number theory is whether a given polynomial equation has integer solutions. We discuss a theorem of Birch who uses the so-called circle method to answer this question for polynomials in 'many' variables. In case there are integer solutions, we study the smallest integer solution. We present new upper bounds on this smallest integer solution, which are obtained using a quantitative version of the Nullstellensatz.

Monday, July 3, 2017

15:30-16:30

BBG 069

Abstract:

Earthquakes can cause substantial damage to buildings in ways that are still not well understood. The amplitude and principal frequency of an earthquake are two primary components that affect the extent of the damage, and they are the basis for many design specification guidelines. We investigate how an external force with varying amplitude and principal frequency affects structurural integrity. As an example we consider a model of a planar, post-tensioned frame that exhibits dynamics quite similar to the experimental measurements of a scaled model on a shake table. The frame remains structurally sound as long as the tilt angle of the frame does not exceed a certain maximum. Many results in the literature are obtained from performing a large number of simulations over a range of amplitudes and frequencies. Such a brute-force approach establishes a region in the frequency-amplitude plane for which the structural stability of the frame eventually fails. Our approach is much more efficient and uses a novel computational method that approximates the failure boundary directly. This method is based on continuation of a suitable two-point boundary value problem. Our computations demonstrate that the failure boundary is only piecewise smooth and the results highlight further interesting details of how the dynamics is organised in the frequency-amplitude plane. We find that failure can occur in profoundly different ways, due to inherent nonlinearities in the system. Stability is particularly affected in a nonlinear way if the natural frequency of the structure is close to that of the external forcing.

Earthquakes can cause substantial damage to buildings in ways that are still not well understood. The amplitude and principal frequency of an earthquake are two primary components that affect the extent of the damage, and they are the basis for many design specification guidelines. We investigate how an external force with varying amplitude and principal frequency affects structurural integrity. As an example we consider a model of a planar, post-tensioned frame that exhibits dynamics quite similar to the experimental measurements of a scaled model on a shake table. The frame remains structurally sound as long as the tilt angle of the frame does not exceed a certain maximum. Many results in the literature are obtained from performing a large number of simulations over a range of amplitudes and frequencies. Such a brute-force approach establishes a region in the frequency-amplitude plane for which the structural stability of the frame eventually fails. Our approach is much more efficient and uses a novel computational method that approximates the failure boundary directly. This method is based on continuation of a suitable two-point boundary value problem. Our computations demonstrate that the failure boundary is only piecewise smooth and the results highlight further interesting details of how the dynamics is organised in the frequency-amplitude plane. We find that failure can occur in profoundly different ways, due to inherent nonlinearities in the system. Stability is particularly affected in a nonlinear way if the natural frequency of the structure is close to that of the external forcing.

Tuesday, July 4, 2017

Tuesday, July 11, 2017

Tuesday, July 18, 2017

Tuesday, July 25, 2017

Tuesday, August 1, 2017

Tuesday, August 8, 2017

Tuesday, August 15, 2017

Tuesday, August 22, 2017

Tuesday, August 29, 2017

Tuesday, September 5, 2017

Tuesday, September 12, 2017

Tuesday, September 19, 2017

Tuesday, September 26, 2017

Thursday, September 28, 2017

16:00-17:00

HFG 610

Tuesday, October 3, 2017

Tuesday, October 10, 2017

16:00-17:00

tba

Tuesday, October 17, 2017

Tuesday, October 24, 2017

Tuesday, October 31, 2017

Tuesday, November 7, 2017

Tuesday, November 14, 2017

16:00-17:00

HFG 610

Tuesday, November 21, 2017

Tuesday, November 28, 2017

Tuesday, December 5, 2017

Tuesday, December 12, 2017

Tuesday, December 19, 2017