IST Austria: PubRep (Institute of Science and Technology)
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Extreme eigenvalues of Laplacian random matrices with Gaussian entries
No full textA Laplacian matrix is a real symmetric matrix whose row and column sums are zero. We investigate the limiting distribution of the largest eigenvalues of a Laplacian random matrix with Gaussian entries. Unlike many classical matrix ensembles, this random matrix model contains dependent entries. Our main results show that the extreme eigenvalues of this model exhibit Poisson statistics. In particular, after properly shifting and scaling, we show that the largest eigenvalue converges to the Gumbel distribution as the dimension of the matrix tends to infinity. While the largest diagonal entry is also shown to have Gumbel fluctuations, there is a rather surprising difference between its deterministic centering term and the centering term required for the largest eigenvalues
Cell-specific wiring routes information flow through hippocampal CA3
No full textThe hippocampus, critical for learning and memory, is dogmatically described as a trisynaptic circuit where dentate gyrus granule cells (GCs), CA3 pyramidal neurons (PNs), and CA1 PNs are serially connected. However, CA3 also forms an autoassociative network, and its PNs have diverse morphologies, intrinsic properties, and GC input levels. How PN subtypes compose this recurrent network is unknown. To determine the synaptic arrangement of identified CA3 PNs, we combine multicellular patch-clamp recording and post hoc morphological analysis in mouse hippocampal slices. PNs can be divided into distinct “superficial” and “deep” subclasses, the latter including previously reported “athorny” cells. Subclasses have distinct input-output transformations and asymmetric connectivity, which is more abundant from superficial to deep PNs, splitting CA3 locally into two parallel recurrent networks. Coincident spontaneous inhibition occurs frequently within but not between subclasses, implying subclass-specific inhibitory innervation. Our results suggest two separately controlled sublayers for parallel information processing in hippocampal CA3
An extension of Muller's sheltering hypothesis for the evolution of sex chromosome gene content
No full textThe first influential hypothesis for sex chromosome evolution was proposed in 1914 by H. J. Muller, who argued that once recombination was suppressed between the X and Y chromosomes, Y-linked genes become “sheltered” from selection, leading to accumulation of recessive loss-of-function (LOF) mutations and decay of Y-linked genes. The hypothesis fell out of favor in the 1970s because early mathematical models failed to support it and data on the dominance of lethal mutations were viewed as incompatible with the hypothesis. We reevaluate the main arguments against Muller's hypothesis and find that they do not conclusively exclude a role for sheltering in sex chromosome evolution. By relaxing restrictive assumptions of earlier models, we show that sheltering promotes fixation of LOF mutations with sexually dimorphic fitness effects, resulting in decay of X-linked genes that are exclusively expressed by males and Y-linked genes that are primarily, though not necessarily exclusively, expressed by females. We further show that drift and other processes contributing to Y degeneration (i.e. selective interference and regulatory evolution) expand conditions of Y-linked gene loss by sheltering. The actual contribution of sheltering to sex chromosome evolution hinges upon the distribution of dominance and sex-specific fitness effects of LOF mutations, which we discuss
Counting rational points on smooth hypersurfaces with high degree
No full textLet X be a smooth projective hypersurface defined over Q. We provide new bounds for rational points of bounded height on X. In particular, we show that if X is a smooth projective hypersurface in Pn with n 4 and degree d 50, then the set of rational points on X of height bounded by B have cardinality On,d,ε (Bn−2+ε ). If X is smooth and has degree d 6, we improve the dimension growth conjecture bound. We achieve an analogue result for affine hypersurfaces whose projective closure is smooth
The first billion years according to JWST
No full textWith stunning clarity, the JWST has revealed the Universe’s first billion years. The scientific community is analysing a wealth of JWST imaging and spectroscopic data from that era, and is in the process of rewriting the astronomy textbooks. Here, as a result of the 2024 ISSI Breakthrough Workshop, we provide a snapshot of the great progress made towards understanding the initial chapters of our cosmic history 1.5 years into the JWST science mission. We present the current census of early galaxies, their luminosities, appearance, chemical composition, masses and formation histories as revealed by JWST. We relate the discovery of massive black holes in early galaxies and discuss their demographics and implications for their formations and growth. We conclude by describing the potential sources of reionization and our current understanding of how the Universe became fully ionized. Throughout the Perspective, we highlight discoveries and breakthroughs, topics and issues that are not yet understood, and questions that will be addressed in the coming years, as JWST continues its revolutionary observations of the early Universe
ARF degradation defines a deeply conserved step in auxin response
No full textIn land plants, the signalling molecule auxin profoundly controls growth and development, chiefly through a transcriptional response system. The auxin response is mediated by modulating the activity of DNA-binding auxin response factor (ARF) proteins. The concentrations and stoichiometry of the competing A- and B-class ARFs define cells’ capacity for auxin response. In the minimal auxin response system of the liverwort Marchantia polymorpha, both A- and B-ARFs are unstable, but the underlying mechanisms, developmental relevance and evolutionary history of this instability are unknown. Here we identify a minimal motif that is necessary for MpARF2 (B-class) degradation and show that it is critical for development and the auxin response. Through comparative analysis and motif swaps among all ARF classes in extant algae and land plants, we infer that the emergence of ARF instability probably occurred in the ancestor of the A- and B-ARF clades and, therefore, preceded or coincided with the origin of the auxin response system
Linear Eigenvalue statistics at the cusp
No full textWe establish universal Gaussian fluctuations for the mesoscopic linear eigenvalue statistics in the vicinity of the cusp-like singularities of the limiting spectral density for Wigner-type random matrices. Prior to this work, the linear eigenvalue statistics at the cusp-like singularities were not studied in any ensemble. Our analysis covers not only the exact cusps but the entire transitionary regime from the square-root singularity at a regular edge through the sharp cusp to the bulk. We identify a new one-parameter family of functionals that govern the limiting bias and variance, continuously interpolating between the previously known formulas in the bulk and at a regular edge. Since cusps are the only possible singularities besides the regular edges, our result gives a complete description of the linear eigenvalue statistics in all regimes
Balancing complexity, performance and plausibility to meta learn plasticity rules in recurrent spiking networks
No full textSynaptic plasticity is a key player in the brain’s life-long learning abilities. However, due to experimental limitations, the mechanistic link between synaptic plasticity rules and the network-level computations they enable remain opaque. Here we use evolutionary strategies (ES) to meta learn local co-active plasticity rules in large recurrent spiking networks with excitatory (E) and inhibitory (I) neurons, using parameterizations of increasing complexity. We discover rules that robustly stabilize network dynamics for all four synapse types acting in isolation (E-to-E, E-to-I, I-to-E and I-to-I). More complex functions such as familiarity detection can also be included in the search constraints. However, our meta learning strategy begins to fail for co-active rules of increasing complexity, as it is challenging to devise loss functions that effectively constrain network dynamics to plausible solutions a priori. Moreover, in line with previous work, we can find multiple degenerate solutions with identical network behaviour. As a local optimization strategy, ES provides one solution at a time and makes exploration of this degeneracy cumbersome. Regardless, we can glean the interdependecies of various plasticity parameters by considering the covariance matrix learned alongside the optimal rule with ES. Our work provides a proof of principle for the success of machine-learning-guided discovery of plasticity rules in large spiking networks, and points at the necessity of more elaborate search strategies going forward
Criticality transition for positive powers of the discrete Laplacian on the half line
No full textWe study the criticality and subcriticality of powers (−Δ) α with α>0 of the discrete Laplacian −Δ acting on ℓ 2 (N). We prove that these positive powers of the Laplacian are critical if and only if α≥3/2. We complement our analysis with Hardy-type inequalities for (−Δ) α in the subcritical regimes α∈(0,3/2). As an illustration of the critical case α≥3/2, we analyze asymptotic properties of discrete eigenvalues emerging by coupling (−Δ) α with a localized potential
The renormalized Nelson model in the weak coupling limit
No full textThe Nelson model describes non-relativistic particles coupled to a relativistic Bose scalar field. In this article, we study the renormalized version of the Nelson model with massless bosons in Davies' weak coupling limit. Our main result states that the two-body Coulomb potential emerges as an effective pair interaction between the particles, which arises from the exchange of virtual excitations of the quantum field