TY - JOUR AB - We prove several results about substructures in Latin squares. First, we explain how to adapt our recent work on high-girth Steiner triple systems to the setting of Latin squares, resolving a conjecture of Linial that there exist Latin squares with arbitrarily high girth. As a consequence, we see that the number of order- n Latin squares with no intercalate (i.e., no 2×2 Latin subsquare) is at least (e−9/4n−o(n))n2. Equivalently, P[N=0]≥e−n2/4−o(n2)=e−(1+o(1))EN , where N is the number of intercalates in a uniformly random order- n Latin square. In fact, extending recent work of Kwan, Sah, and Sawhney, we resolve the general large-deviation problem for intercalates in random Latin squares, up to constant factors in the exponent: for any constant 0<δ≤1 we have P[N≤(1−δ)EN]=exp(−Θ(n2)) and for any constant δ>0 we have P[N≥(1+δ)EN]=exp(−Θ(n4/3logn)). Finally, as an application of some new general tools for studying substructures in random Latin squares, we show that in almost all order- n Latin squares, the number of cuboctahedra (i.e., the number of pairs of possibly degenerate 2×2 submatrices with the same arrangement of symbols) is of order n4, which is the minimum possible. As observed by Gowers and Long, this number can be interpreted as measuring ``how associative'' the quasigroup associated with the Latin square is. AU - Kwan, Matthew Alan AU - Sah, Ashwin AU - Sawhney, Mehtaab AU - Simkin, Michael ID - 14444 IS - 2 JF - Israel Journal of Mathematics SN - 0021-2172 TI - Substructures in Latin squares VL - 256 ER - TY - CONF AB - As AI and machine-learned software are used increasingly for making decisions that affect humans, it is imperative that they remain fair and unbiased in their decisions. To complement design-time bias mitigation measures, runtime verification techniques have been introduced recently to monitor the algorithmic fairness of deployed systems. Previous monitoring techniques assume full observability of the states of the (unknown) monitored system. Moreover, they can monitor only fairness properties that are specified as arithmetic expressions over the probabilities of different events. In this work, we extend fairness monitoring to systems modeled as partially observed Markov chains (POMC), and to specifications containing arithmetic expressions over the expected values of numerical functions on event sequences. The only assumptions we make are that the underlying POMC is aperiodic and starts in the stationary distribution, with a bound on its mixing time being known. These assumptions enable us to estimate a given property for the entire distribution of possible executions of the monitored POMC, by observing only a single execution. Our monitors observe a long run of the system and, after each new observation, output updated PAC-estimates of how fair or biased the system is. The monitors are computationally lightweight and, using a prototype implementation, we demonstrate their effectiveness on several real-world examples. AU - Henzinger, Thomas A AU - Kueffner, Konstantin AU - Mallik, Kaushik ID - 14454 SN - 0302-9743 T2 - 23rd International Conference on Runtime Verification TI - Monitoring algorithmic fairness under partial observations VL - 14245 ER - TY - JOUR AB - Recent work has paid close attention to the first principle of Granger causality, according to which cause precedes effect. In this context, the question may arise whether the detected direction of causality also reverses after the time reversal of unidirectionally coupled data. Recently, it has been shown that for unidirectionally causally connected autoregressive (AR) processes X → Y, after time reversal of data, the opposite causal direction Y → X is indeed detected, although typically as part of the bidirectional X↔ Y link. As we argue here, the answer is different when the measured data are not from AR processes but from linked deterministic systems. When the goal is the usual forward data analysis, cross-mapping-like approaches correctly detect X → Y, while Granger causality-like approaches, which should not be used for deterministic time series, detect causal independence X → Y. The results of backward causal analysis depend on the predictability of the reversed data. Unlike AR processes, observables from deterministic dynamical systems, even complex nonlinear ones, can be predicted well forward, while backward predictions can be difficult (notably when the time reversal of a function leads to one-to-many relations). To address this problem, we propose an approach based on models that provide multiple candidate predictions for the target, combined with a loss function that consideres only the best candidate. The resulting good forward and backward predictability supports the view that unidirectionally causally linked deterministic dynamical systems X → Y can be expected to detect the same link both before and after time reversal. AU - Jakubík, Jozef AU - Bui Thi Mai, Phuong AU - Chvosteková, Martina AU - Krakovská, Anna ID - 14446 IS - 4 JF - Measurement Science Review TI - Against the flow of time with multi-output models VL - 23 ER - TY - JOUR AB - We study the Fröhlich polaron model in R3, and establish the subleading term in the strong coupling asymptotics of its ground state energy, corresponding to the quantum corrections to the classical energy determined by the Pekar approximation. AU - Brooks, Morris AU - Seiringer, Robert ID - 14441 JF - Communications in Mathematical Physics SN - 0010-3616 TI - The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy VL - 404 ER - TY - CONF AB - We consider the problem of solving LP relaxations of MAP-MRF inference problems, and in particular the method proposed recently in [16], [35]. As a key computational subroutine, it uses a variant of the Frank-Wolfe (FW) method to minimize a smooth convex function over a combinatorial polytope. We propose an efficient implementation of this subroutine based on in-face Frank-Wolfe directions, introduced in [4] in a different context. More generally, we define an abstract data structure for a combinatorial subproblem that enables in-face FW directions, and describe its specialization for tree-structured MAP-MRF inference subproblems. Experimental results indicate that the resulting method is the current state-of-art LP solver for some classes of problems. Our code is available at pub.ist.ac.at/~vnk/papers/IN-FACE-FW.html. AU - Kolmogorov, Vladimir ID - 14448 SN - 1063-6919 T2 - Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition TI - Solving relaxations of MAP-MRF problems: Combinatorial in-face Frank-Wolfe directions VL - 2023 ER - TY - JOUR AB - Cytosine methylation within CG dinucleotides (mCG) can be epigenetically inherited over many generations. Such inheritance is thought to be mediated by a semiconservative mechanism that produces binary present/absent methylation patterns. However, we show here that in Arabidopsis thaliana h1ddm1 mutants, intermediate heterochromatic mCG is stably inherited across many generations and is quantitatively associated with transposon expression. We develop a mathematical model that estimates the rates of semiconservative maintenance failure and de novo methylation at each transposon, demonstrating that mCG can be stably inherited at any level via a dynamic balance of these activities. We find that DRM2 – the core methyltransferase of the RNA-directed DNA methylation pathway – catalyzes most of the heterochromatic de novo mCG, with de novo rates orders of magnitude higher than previously thought, whereas chromomethylases make smaller contributions. Our results demonstrate that stable epigenetic inheritance of mCG in plant heterochromatin is enabled by extensive de novo methylation. AU - Lyons, David B. AU - Briffa, Amy AU - He, Shengbo AU - Choi, Jaemyung AU - Hollwey, Elizabeth AU - Colicchio, Jack AU - Anderson, Ian AU - Feng, Xiaoqi AU - Howard, Martin AU - Zilberman, Daniel ID - 12672 IS - 3 JF - Cell Reports TI - Extensive de novo activity stabilizes epigenetic inheritance of CG methylation in Arabidopsis transposons VL - 42 ER - TY - JOUR AB - We consider the large polaron described by the Fröhlich Hamiltonian and study its energy-momentum relation defined as the lowest possible energy as a function of the total momentum. Using a suitable family of trial states, we derive an optimal parabolic upper bound for the energy-momentum relation in the limit of strong coupling. The upper bound consists of a momentum independent term that agrees with the predicted two-term expansion for the ground state energy of the strongly coupled polaron at rest and a term that is quadratic in the momentum with coefficient given by the inverse of twice the classical effective mass introduced by Landau and Pekar. AU - Mitrouskas, David Johannes AU - Mysliwy, Krzysztof AU - Seiringer, Robert ID - 13178 JF - Forum of Mathematics TI - Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron VL - 11 ER - TY - JOUR AB - Intercellular signaling molecules, known as morphogens, act at a long range in developing tissues to provide spatial information and control properties such as cell fate and tissue growth. The production, transport, and removal of morphogens shape their concentration profiles in time and space. Downstream signaling cascades and gene regulatory networks within cells then convert the spatiotemporal morphogen profiles into distinct cellular responses. Current challenges are to understand the diverse molecular and cellular mechanisms underlying morphogen gradient formation, as well as the logic of downstream regulatory circuits involved in morphogen interpretation. This knowledge, combining experimental and theoretical results, is essential to understand emerging properties of morphogen-controlled systems, such as robustness and scaling. AU - Kicheva, Anna AU - Briscoe, James ID - 14484 JF - Annual Review of Cell and Developmental Biology SN - 1081-0706 TI - Control of tissue development by morphogens VL - 39 ER - TY - JOUR AB - Portrait viewpoint and illumination editing is an important problem with several applications in VR/AR, movies, and photography. Comprehensive knowledge of geometry and illumination is critical for obtaining photorealistic results. Current methods are unable to explicitly model in 3D while handling both viewpoint and illumination editing from a single image. In this paper, we propose VoRF, a novel approach that can take even a single portrait image as input and relight human heads under novel illuminations that can be viewed from arbitrary viewpoints. VoRF represents a human head as a continuous volumetric field and learns a prior model of human heads using a coordinate-based MLP with individual latent spaces for identity and illumination. The prior model is learned in an auto-decoder manner over a diverse class of head shapes and appearances, allowing VoRF to generalize to novel test identities from a single input image. Additionally, VoRF has a reflectance MLP that uses the intermediate features of the prior model for rendering One-Light-at-A-Time (OLAT) images under novel views. We synthesize novel illuminations by combining these OLAT images with target environment maps. Qualitative and quantitative evaluations demonstrate the effectiveness of VoRF for relighting and novel view synthesis, even when applied to unseen subjects under uncontrolled illumination. This work is an extension of Rao et al. (VoRF: Volumetric Relightable Faces 2022). We provide extensive evaluation and ablative studies of our model and also provide an application, where any face can be relighted using textual input. AU - Rao, Pramod AU - Mallikarjun, B. R. AU - Fox, Gereon AU - Weyrich, Tim AU - Bickel, Bernd AU - Pfister, Hanspeter AU - Matusik, Wojciech AU - Zhan, Fangneng AU - Tewari, Ayush AU - Theobalt, Christian AU - Elgharib, Mohamed ID - 14488 JF - International Journal of Computer Vision SN - 0920-5691 TI - A deeper analysis of volumetric relightiable faces ER - TY - JOUR AB - High Mountain Asia (HMA) is among the most vulnerable water towers globally and yet future projections of water availability in and from its high-mountain catchments remain uncertain, as their hydrologic response to ongoing environmental changes is complex. Mechanistic modeling approaches incorporating cryospheric, hydrological, and vegetation processes in high spatial, temporal, and physical detail have never been applied for high-elevation catchments of HMA. We use a land surface model at high spatial and temporal resolution (100 m and hourly) to simulate the coupled dynamics of energy, water, and vegetation for the 350 km2 Langtang catchment (Nepal). We compare our model outputs for one hydrological year against a large set of observations to gain insight into the partitioning of the water balance at the subseasonal scale and across elevation bands. During the simulated hydrological year, we find that evapotranspiration is a key component of the total water balance, as it causes about the equivalent of 20% of all the available precipitation or 154% of the water production from glacier melt in the basin to return directly to the atmosphere. The depletion of the cryospheric water budget is dominated by snow melt, but at high elevations is primarily dictated by snow and ice sublimation. Snow sublimation is the dominant vapor flux (49%) at the catchment scale, accounting for the equivalent of 11% of snowfall, 17% of snowmelt, and 75% of ice melt, respectively. We conclude that simulations should consider sublimation and other evaporative fluxes explicitly, as otherwise water balance estimates can be ill-quantified. AU - Buri, Pascal AU - Fatichi, Simone AU - Shaw, Thomas AU - Miles, Evan S. AU - Mccarthy, Michael AU - Fyffe, Catriona Louise AU - Fugger, Stefan AU - Ren, Shaoting AU - Kneib, Marin AU - Jouberton, Achille AU - Steiner, Jakob AU - Fujita, Koji AU - Pellicciotti, Francesca ID - 14487 IS - 10 JF - Water Resources Research SN - 0043-1397 TI - Land surface modeling in the Himalayas: On the importance of evaporative fluxes for the water balance of a high-elevation catchment VL - 59 ER -