Miracle-dz/UniFAR-FTUs huggingface dataset:
Quantization of systems with temporally varying discretization. II. Local evolution moves

Several quantum gravity approaches and field theory on an evolving lattice involve a discretization changing dynamics generated by evolution moves. Local evolution moves in variational discrete systems (1) are a generalization of the Pachner evolution moves of simplicial gravity models, (2) update only a small subset of the dynamical data, (3) change the number of kinematical and physical degrees of freedom, and (4) generate a dynamical (or canonical) coarse graining or refining of the underlying discretization. To systematically explore such local moves and their implications in the quantum theory, this article suitably expands the quantum formalism for global evolution moves, constructed in Paper I [P. A. Hohn, “Quantization of systems with temporally varying discretization. I. Evolving Hilbert spaces,” J. Math. Phys.55, 083508 (2014); e-print arXiv:1401.6062 [gr-qc]], by employing that global moves can be decomposed into sequences of local moves. This formalism is spelled out for systems with Euclidean configuration spaces. Various types of local moves, the different kinds of constraints generated by them, the constraint preservation, and possible divergences in resulting state sums are discussed. It is shown that non-trivial local coarse graining moves entail a non-unitary projection of (physical) Hilbert spaces and “fine grained” Dirac observables defined on them. Identities for undoing a local evolution move with its (time reversed) inverse are derived. Finally, the implications of these results for a Pachner move generated dynamics in simplicial quantum gravity models are commented on.
Resonant normal form and asymptotic normal form behaviour in magnetic bottle Hamiltonians

We consider normal forms in ‘magnetic bottle’ type Hamiltonians of the form (second frequency ω2 equal to zero in the lowest order). Our main results are: (i) a novel method to construct the normal form in cases of resonance, and (ii) a study of the asymptotic behaviour of both the non-resonant and the resonant series. We find that, if we truncate the normal form series at order r, the series remainder in both constructions decreases with increasing r down to a minimum, and then it increases with r. The computed minimum remainder turns to be exponentially small in , where ΔE is the mirror oscillation energy, while the optimal order scales as an inverse power of ΔE. We estimate numerically the exponents associated with the optimal order and the remainder's exponential asymptotic behaviour. In the resonant case, our novel method allows to compute a ‘quasi-integral’ (i.e. truncated formal integral) valid both for each particular resonance as well as away from all resonances. We applied these results to a specific magnetic bottle Hamiltonian. The non-resonant normal form yields theoretical invariant curves on a surface of section which fit well the empirical curves away from resonances. On the other hand the resonant normal form fits very well both the invariant curves inside the islands of a particular resonance as well as the non-resonant invariant curves. Finally, we discuss how normal forms allow to compute a critical threshold for the onset of global chaos in the magnetic bottle.
Definition of Urban Built Environment Climate Adaptive Design Actions Aided by Environmental Data-Driven Design Processes

Environmental and technological design for climate adaptation in the urban built environment can no longer be separated from the generation, collection, or use of data (big data). ICT tools (Information and Communication Technologies), for the modelling and simulation of the built urban environment are identified as measuring devices and provide knowledge on the impacts of climate change in design practice based on an environmentally data-driven approach. This study aims to define a framework for the evaluation of environmental health and comfort parameters applicable to simulation tools, with a specific focus on thermal and environmental exchanges between indoor and outdoor spaces, to define those factors that affect the perception of user’s well-being in thermal stress conditions (e.g., heatwaves), both indoor and outdoor. Through the definition of two study cases in the city of Naples, Italy, special attention was paid to investigating the interaction between outdoor and indoor performance when urban temperatures rise. A comparison between a daily survey for occupants and simulations was conducted to confirm the validity of the data obtainable from the perceived thermal sensations. The obtained results show that the designed framework can reliably simulate real outdoor and indoor conditions according to comfort indices such as the predicted mean vote and adaptive comfort model. The methodological framework developed can guarantee the interoperability of data to simulate indoor and outdoor environments responding to real conditions and determine a favourable condition for the development of urban redevelopment interventions through the application of climate adaptive design strategies.
Paradoxical Motor

Marinov’s proposals involve use of two half-cylindrical magnets, axially polarized in opposite directions, surrounded by a solid (left figure) or liquid (right figure) annular conductor that is connected at two diametrically opposite points to a battery (via sliding contacts in case of the sold ring conductor which is free to rotate about its axis). Marinov was unable to make his proposed motor work, and committed suicide in 1997. But within months of this tragic event the motor was shown to work in [3], which included the figure on the top left of the next page. Most likely, the apparatus used in [3] was similar to that in the top right figure on the next page (from [13]), in which two axially, oppositely magnetized stacks of disk magnets were joined by two “keepers” to form an approximation to a toroidal magnet. The Maxwellian view is that the magnetic field is zero outside a toroidal magnet, so it is paradoxical that a torque could be exerted on the ring rotor to drive the motor.
Extremal K\"ahler metrics

This paper is a survey of some recent progress on the study of Calabi's extremal K\"ahler metrics. We first discuss the Yau-Tian-Donaldson conjecture relating the existence of extremal metrics to an algebro-geometric stability notion and we give some example settings where this conjecture has been established. We then turn to the question of what one expects when no extremal metric exists.
The Maximum Number of Cycles in a Graph with Fixed Number of Edges

The main problem considered in this paper is maximizing the number of cycles in a graph with given number of edges. In 2009, Király conjectured that there is constant $c$ such that any graph with $m$ edges has at most $c(1.4)^m$ cycles. In this paper, it is shown that for sufficiently large $m$, a graph with $m$ edges has at most $(1.443)^m$ cycles. For sufficiently large $m$, examples of a graph with $m$ edges and $(1.37)^m$ cycles are presented. For a graph with given number of vertices and edges an upper bound on the maximal number of cycles is given. Also, bounds tight up to a constant are presented for the maximum number of cycles in a multigraph with given number of edges, as well as in a multigraph with given number of vertices and edges.
A generalization of the extremal function of the Davenport-Schinzel sequences

Let $[n]=\{1, \ldots, n\}$. A sequence $u=a_1a_2\dots a_l$ over $[n]$ is called $k$-sparse if $a_i = a_j$, $i > j$ implies $i-j\geq k$. In other words, every consecutive subsequence of $u$ of length at most $k$ does not have letters in common. Let $u,v$ be two sequences. We say that $u$ is $v$-free, if $u$ does not contain a subsequence isomorphic to $v$. Suppose there are only $k$ letters appearing in $v$. The extremal function Ex$(v,n)$ is defined as the maximum length of all the $v$-free and $k$-sparse sequences. In this paper, we study a generalization of the extremal function Ex$(v,n)$.
Semi-direct product of groups, filter banks and sampling

An abstract sampling theory associated to a unitary representation of a countable discrete non abelian group $G$, which is a semi-direct product of groups, on a separable Hilbert space is studied. A suitable expression of the data samples and the use of a filter bank formalism allows to fix the mathematical problem to be solved: the search of appropriate dual frames for $\ell^2(G)$. An example involving crystallographic groups illustrates the obtained results by using average or pointwise samples.
UvA-DARE Dynamic Adaptive Approach to Transportation-Infrastructure Planning for Climate Change: San-Francisco-Bay-Area Case Study

: Adaptation of existing infrastructure is a response to climate change that can ensure a viable, safe, and robust transportation network. However, deep uncertainties associated with climate change pose significant challenges to adaptation planning. Specifically, current transportation planning methods are ill-equipped to address deep uncertainties, as they rely on designing responses to a few predicted futures, none of which will occur exactly as envisioned. In this paper, we propose using dynamic adaptive planning (DAP), an emerging general strategic planning method, to account for deep uncertainties by building flexibility and learning mechanisms into plans that enable continuous adaptation throughout implementation. This paper first reviews uncertainty in general, introduces what is meant by deep uncertainty , and then introduces DAP. Then, DAP is applied to a case study of the Oakland approach to the San Francisco-Oakland Bay Bridge, which was initially assessed under the 2010 – 2011 FHWA Climate Change Vulnerability Assessment Pilot program, to illustrate how DAP could be applied as a response to climate change in the context of evolving transportation infrastructure adaptation planning practices in the United States. We conclude that DAP is well suited to account for the deep uncertainties of climate change in transportation and infrastructure planning, and provide suggestions for further research to better apply DAP in this field. DOI: 10.1061/(ASCE)IS.1943-555X.0000257. © 2015 American Society of Civil Engineers.
Phantom Maps and Finiteness Conditions

A phantom map is a potentially nontrivial map which induces the zero map on every homology theory and on homotopy groups. Zabrodsky has shown that in the presence of particular finiteness conditions on spaces $X$ and $Y$ every map $X\to Y$ is a phantom map. More specifically, Zabrodsky essentially requires $Y$ to be a finite CW complex and $X$ to be a Postnikov space. We show Zabrodsky's observations hold under less restrictive finiteness conditions on the spaces $X$ and $Y$, making use of the Zabrodsky lemma and the machinery of resolving classes. As an application we identify, up to extension, the group of self-homotopy equivalences of spaces belonging to a particular family.
Task Fusion in Distributed Runtimes

We present distributed task fusion, a run-time optimization for task-based runtimes operating on parallel and heterogeneous systems. Distributed task fusion dynamically performs an efficient buffering, analysis, and fusion of asynchronously-evaluated distributed operations, reducing the overheads inherent to scheduling distributed tasks in implicitly parallel frameworks and runtimes. We identify the constraints under which distributed task fusion is permissible and describe an implementation in Legate, a domain-agnostic library for constructing portable and scalable task-based libraries. We present performance results using cuNumeric, a Legate library that enables scalable execution of NumPy pipelines on parallel and heterogeneous systems. We realize speedups up to 1.5x with task fusion enabled on up to 32 P100 GPUs, thus demonstrating efficient execution of pipelines involving many successive fine-grained tasks. Finally, we discuss potential future work, including complementary optimizations that could result in additional performance improvements.
The Galerkin Method for Perturbed Self-Adjoint Operators and Applications

We consider the Galerkin method for approximating the spectrum of an operator $T+A$ where $T$ is semi-bounded self-adjoint and $A$ satisfies a relative compactness condition. We show that the method is reliable in all regions where it is reliable for the unperturbed problem - which always contains $\mathbb{C}\backslash\mathbb{R}$. The results lead to a new technique for identifying eigenvalues of $T$, and for identifying spectral pollution which arises from applying the Galerkin method directly to $T$. The new technique benefits from being applicable on the form domain.
Uniqueness Estimates for the General Complex Conductivity Equation and Their Applications to Inverse Problems

The aim of the paper is twofold. Firstly, we would like to derive quantitative uniqueness estimates for solutions of the general complex conductivity equation. It is still unknown whether the \emph{strong} unique continuation property holds for such equations. Nonetheless, in this paper, we show that the unique continuation property in the form of three-ball inequalities is satisfied for the complex conductivity equation under only Lipschitz assumption on the leading coefficients. The derivation of such estimates relies on a delicate Carleman estimate. Secondly, we study the problem of estimating the size of an inclusion embedded inside of a conductive body with anisotropic complex admittivity by one boundary measurement. The study of such inverse problem is motivated by practical problems.
Monte Carlo Methods for Insurance Risk Computation

In this paper we consider the problem of computing tail probabilities of the distribution of a random sum of positive random variables. We assume that the individual claim variables follow a reproducible natural exponential family (NEF) distribution, and that the random number has a NEF counting distribution with a cubic variance function. This specific modeling is supported by data of the aggregated claim distribution of an insurance company. Large tail probabilities are important as they reflect the risk of large losses, however, analytic or numerical expressions are not available. We propose several simulation algorithms which are based on an asymptotic analysis of the distribution of the counting variable and on the reproducibility property of the claim distribution. The aggregated sum is simulated efficiently by importance sampling using an exponential change of measure. We conclude by numerical experiments of these algorithms, based on real car insurance claim data.
Robustness in deep learning: The width (good), the depth (bad), and the initialization (ugly)

We study the average robustness notion in deep neural networks in (selected) wide and narrow, deep and shallow, as well as lazy and non-lazy training settings. We prove that in the under-parameterized setting, width has a negative effect while it improves robustness in the over-parameterized setting. The effect of depth closely depends on the initialization and the training mode. In particular, when initialized with Le-Cun initialization, depth helps robustness with lazy training regime. In contrast, when initialized with Neural Tangent Kernel (NTK) and He-initialization, depth exacerbates the robustness. Moreover, under non-lazy training regime, we demonstrate how the width of a two-layer ReLU network benefits robustness. Our theoretical developments improve the results by Huang et al. (2021); Wu et al. (2021) and are consistent with Bubeck and Sellke (2021); Bubeck et al. (2021).
Viscosity of CO2-bearing silicate melts at high pressure

Viscosity is an important property of magma (silicate melt), because it controls the transportation of magma in the planetary interior. Traditionally, viscosity at high pressure was measured in quenching experiments. At the beginning a metallic sphere was places at the top of a sample chamber. The falling velocity was determined from the falling distance during the molten period of sample. The movement of a metallic sphere in a sample chamber was recorded in X-ray radiography image. We have used this technique to determine the pressure, temperature and compositional dependence of the viscosity of silicate melts. The main goal of our study is to determine the effect of dissolving carbon dioxide on the viscosity of silicate melts at high pressure. It has been known that volatiles are dissolved in natural magmas and affects the physical properties. However, very few studies have been performed to investigate the effect of carbon dioxide on the viscosity of silicate melts at mantle pressures. In the present study, the viscosity of carbon-dioxide bearing CaMgSi2O6 and NaAlSi2O6 composition melts have been determined up to 5 GPa. We installed an X-ray radiography system at the NE7A station at High Energy Accelerator Research Organization (KEK) in Tsukuba, Japan. A charge? coupled device (CCD) camera with a YAG:Ce ﬂuorescence screen was used to obtain the X-ray absorption contrast image. High-pressure was generated using a Kawai type multi-anvil apparatus, which was driven by a DIA type guide block in the MAX-III system. The pressure was determined by using an equation of state for MgO. A pure-Ge solid sate detector was used to collect the X-ray diffraction data of the pressure standard by energy-dispersive method. The starting mixture was synthesized from reagents at 1 atm. A powder mixture of oxides and carbonates were fused and quenched to make a glass. Carbonate powder was ﬁnally added as a source of carbon dioxide. Structural study has suggested that the CaMgSi2O6 composition melt is depolymerized. The viscosity of pure CaMgSi2O6 melt increases with increasing pressure. By the addition of 1.0 wt % of carbon dioxide produces about 50% decrease under pressure. NaAlSi2O6 composition melt has polymerized structure. In our previous study, we observed the decrease of viscosity of the pure NaAlSi2O6 melt with elevating pressure. In this study, we measured the viscosity of NaAlSi2O6 + 0.5 wt% CO2 melt. The viscosity of CO2-bearing NaAlSi2O6 melt decreases by about one order of magnitude. Our results suggest that the viscosity of the polymerized silicate and aluminosilicate melts are relatively reduced by the addition of CO2, because CO2 depolymerizes the SiO4 and AlO4 networks.
Extinction time of the logistic process

Abstract The logistic birth and death process is perhaps the simplest stochastic population model that has both density-dependent reproduction and a phase transition, and a lot can be learned about the process by studying its extinction time, $\tau_n$ , as a function of system size n. A number of existing results describe the scaling of $\tau_n$ as $n\to\infty$ for various choices of reproductive rate $r_n$ and initial population $X_n(0)$ as a function of n. We collect and complete this picture, obtaining a complete classification of all sequences $(r_n)$ and $(X_n(0))$ for which there exist rescaling parameters $(s_n)$ and $(t_n)$ such that $(\tau_n-t_n)/s_n$ converges in distribution as $n\to\infty$ , and identifying the limits in each case.
Invariant perfect tensors

Invariant tensors are states in the SU(2) tensor product representation that are invariant under SU(2) action. They play an important role in the study of loop quantum gravity. On the other hand, perfect tensors are highly entangled many-body quantum states with local density matrices maximally mixed. Recently, the notion of perfect tensors has attracted a lot of attention in the fields of quantum information theory, condensed matter theory, and quantum gravity. In this work, we introduce the concept of an invariant perfect tensor (IPT), which is an n-valent tensor that is both invariant and perfect. We discuss the existence and construction of IPTs. For bivalent tensors, the IPT is the unique singlet state for each local dimension. The trivalent IPT also exists and is uniquely given by Wigner’s 3 j symbol. However, we show that, surprisingly, 4-valent IPTs do not exist for any identical local dimension d. On the contrary, when the dimension is large, almost all invariant tensors are asymptotically perfect, which is a consequence of the phenomenon of the concentration of measure for multipartite quantum states.
Indirect (source-free) integration method. I. Wave-forms from geodesic generic orbits of EMRIs

The Regge-Wheeler-Zerilli (RWZ) wave-equation describes Schwarzschild-Droste black hole perturbations. The source term contains a Dirac distribution and its derivative. We have previously designed a method of integration in time domain. It consists of a finite difference scheme where analytic expressions, dealing with the wave-function discontinuity through the jump conditions, replace the direct integration of the source and the potential. Herein, we successfully apply the same method to the geodesic generic orbits of EMRI (Extreme Mass Ratio Inspiral) sources, at second order. An EMRI is a Compact Star (CS) captured by a Super Massive Black Hole (SMBH). These are considered the best probes for testing gravitation in strong regime. The gravitational wave-forms, the radiated energy and angular momentum at infinity are computed and extensively compared with other methods, for different orbits (circular, elliptic, parabolic, including zoom-whirl).
Free energy in the mixed p-spin models with vector spins

Using the synchronization mechanism developed in the previous work on the Potts spin glass model, arXiv:1512.00370, we obtain the analogue of the Parisi formula for the free energy in the mixed even $p$-spin models with vector spins, which include the Sherrington-Kirkpatrick model with vector spins interacting through their scalar product. As a special case, this also establishes the sharpness of Talagrand's upper bound for the free energy of multiple mixed $p$-spin systems coupled by constraining their overlaps.
Consistency and derangements in brane tilings

Brane tilings describe Lagrangians (vector multiplets, chiral multiplets, and the superpotential) of four-dimensional  = 1 supersymmetric gauge theories. These theories, written in terms of a bipartite graph on a torus, correspond to worldvolume theories on N D3-branes probing a toric Calabi–Yau threefold singularity. A pair of permutations compactly encapsulates the data necessary to specify a brane tiling. We show that geometric consistency for brane tilings, which ensures that the corresponding quantum field theories are well behaved, imposes constraints on the pair of permutations, restricting certain products constructed from the pair to have no one-cycles. Permutations without one-cycles are known as derangements. We illustrate this formulation of consistency with known brane tilings. Counting formulas for consistent brane tilings with an arbitrary number of chiral bifundamental fields are written down in terms of delta functions over symmetric groups.
Singularity of generalized grey Brownian motion and time-changed Brownian motion

The generalized grey Brownian motion is a time continuous self-similar with stationary increments stochastic process whose one dimensional distributions are the fundamental solutions of a stretched time fractional differential equation. Moreover, the distribution of the time-changed Brownian motion by an inverse stable process solves the same equation, hence both processes have the same one dimensional distribution. In this paper we show the mutual singularity of the probability measures on the path space which are induced by generalized grey Brownian motion and the time-changed Brownian motion though they have the same one dimensional distribution. This singularity property propagates to the probability measures of the processes which are solutions to the stochastic differential equations driven by these processes.