Publication

Counting Intersecting and Pairs of Cross-Intersecting Families

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In this paper, we consider the first eigenvalue.1(O) of the Grushin operator.G :=.x1 + |x1|2s.x2 with Dirichlet boundary conditions on a bounded domain O of Rd = R d1+ d2. We prove that.1(O) admits a unique minimizer in the class of domains with prescribed ...

WALTER DE GRUYTER GMBH2023

Neuromodulation of neocortical microcircuitry: a multi-scale framework to model the effects of cholinergic release

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Neuromodulation of neocortical microcircuits is one of the most fascinating and mysterious aspects of brain physiology. Despite over a century of research, the neuroscientific community has yet to uncover the fundamental biological organizing principles un ...

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Let K be a totally real number field of degree n >= 2. The inverse different of K gives rise to a lattice in Rn. We prove that the space of Schwartz Fourier eigenfunctions on R-n which vanish on the "component-wise square root" of this lattice, is infinite ...

EUROPEAN MATHEMATICAL SOC-EMS2022

Guidelines for performing lignin-first biorefining

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The valorisation of the plant biopolymer lignin is now recognised as essential to enabling the economic viability of the lignocellulosic biorefining industry. In this context, the "lignin-first" biorefining approach, in which lignin valorisation is conside ...

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Physics-enhanced machine learning with symmetry-adapted and long-range representations

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Theoretical and computational approaches to the study of materials and molecules have, over the last few decades, progressed at an exponential rate. Yet, the possibility of producing numerical predictions that are on par with experimental measurements is t ...

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Flow Path Optimization for Soft Pneumatic Actuators: Towards Optimal Performance and Portability

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Soft pneumatic actuators (SPAs) are highly desirable for interactive robotics applications owing to their unconventional properties like high compliance, safe human-machine interaction and adaptable design space. The SPA dynamic behaviour is governed by pn ...

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Free Boundary Regularity for Almost Every Solution to the Signorini Problem

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We investigate the regularity of the free boundary for the Signorini problem in Rn+1. It is known that regular points are (n−1)-dimensional and C∞. However, even for C∞ obstacles φ, the set of non-regular (or degenerate) points could be very large—e.g. wit ...

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Model-Based Interpretation of Measurements for Fatigue Evaluation of Existing Reinforced Concrete Bridges

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New methods are required for sustainable and economical management of bridges. Efficient management can be achieved by a detailed understanding of bridge behavior through monitoring and model-based data interpretation. This paper presents a methodology to ...

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An Ink–and–Paper Automaton: The Conceptual Mechanization of Cognition and the Practical Automation of Reasoning in Leibniz’s De Affectibus (1679)

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On ten loose handwritten folios dating back from April 1679, Leibniz gradually devised, in the course of three days, a full-blown theory of thought that nonetheless remained unpublished and still has received little attention from scholars. Conceiving of a ...

2020

Packing the Boolean lattice with copies of a poset

Istvan Tomon

The Boolean lattice (2[n],subset of) is the family of all subsets of [n]={1,MIDLINE HORIZONTAL ELLIPSIS,n}, ordered by inclusion. Let P be a partially ordered set. We prove that if n is sufficiently large, then there exists a packing P of copies of P in (2 ...

WILEY2020

Wasserstein Distributionally Robust Learning

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Many decision problems in science, engineering, and economics are affected by uncertainty, which is typically modeled by a random variable governed by an unknown probability distribution. For many practical applications, the probability distribution is onl ...

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Cross-sections of line configurations in R-3 and (d-2)-flat configurations in R-d

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We consider sets L = {l(1),..., l(n)} of n labeled lines in general position in R-3, and study the order types of point sets {p(1),..., p(n)} that stem from the intersections of the lines in L with (directed) planes Pi, not parallel to any line of L, that ...

ELSEVIER SCIENCE BV2019

Design of Load-Bearing Systems for Open-Ended Downstream Reuse

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2019

Forbidden induced subposets of given height

Istvan Tomon

Let P be a partially ordered set. The function La* (n, P) denotes the size of the largest family F subset of 2([n]) that does not contain an induced copy of P. It was proved by Methuku and Palvolgyi that there exists a constant C-P (depending only on P) su ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2019

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It is proved that the total length of any set of countably many rectifiable curves whose union meets all straight lines that intersect the unit square U is at least 2.00002. This is the first improvement on the lower bound of 2 known since 1964. A similar ...

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On the Number of Containments in P-free Families

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A subfamily {F-1, F-2, ..., F-vertical bar P vertical bar} subset of F is a copy of the poset P if there exists a bijection i : P -> {F-1, F-2, ..., F-vertical bar P vertical bar}, such that p

Springer2019

Construction of Polar Codes With Sublinear Complexity

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Consider the problem of constructing a polar code of block length N for a given transmission channel W. Previous approaches require one to compute the reliability of the N synthetic channels and then use only those that are sufficiently reliable. However, ...

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The need for predictive capabilities greater than 95% with very limited false alarms are demanding requirements for reliable disruption prediction systems in tokamaks such as JET or, in the near future, ITER. The prediction of an upcoming disruption must b ...

IOP Publishing Ltd2019

Matching fields and lattice points of simplices

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We show that the Chow covectors of a linkage matching field define a bijection of lattice points and we demonstrate how one can recover the linkage matching field from this bijection. This resolves two open questions from Sturmfels & Zelevinsky (1993) on l ...

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On Sets Defining Few Ordinary Circles

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An ordinary circle of a set P of n points in the plane is defined as a circle that contains exactly three points of P. We show that if P is not contained in a line or a circle, then P spans at least ordinary circles. Moreover, we determine the exact minimu ...

Springer2018