Geometric characterization of the persistence of 1D maps.

We characterize critical points of 1-dimensional maps paired in persistent homology geometrically and this way get elementary proofs of theorems about the symmetry of persistence diagrams and the variation of such maps. In particular, we identify branching points and endpoints of networks as the sole source of asymmetry and relate the cycle basis in persistent homology with a version of the stable marriage problem. Our analysis provides the foundations of fast algorithms for maintaining a collection of sorted lists together with its persistence diagram.

On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane.

For a locally finite set in , the order- Brillouin tessellations form an infinite sequence of convex face-to-face tilings of the plane. If the set is coarsely dense and generic, then the corresponding infinite sequences of minimum and maximum angles are both monotonic in . As an example, a stationary Poisson point process in is locally finite, coarsely dense, and generic with probability one.

Depth in arrangements: Dehn-Sommerville-Euler relations with applications.

The depth of a cell in an arrangement of (non-vertical) great-spheres in is the number of great-spheres that pass above the cell. We prove Euler-type relations, which imply extensions of the classic Dehn-Sommerville relations for convex polytopes to sublevel sets of the depth function, and we use the relations to extend the expressions for the number of faces of neighborly polytopes to the number of cells of levels in neighborly arrangements.

Computing the Multicover Bifiltration.

Given a finite set , let denote the set of all points within distance to at least points of . Allowing and to vary, we obtain a 2-parameter family of spaces that grow larger when increases or decreases, called the . Motivated by the problem of computing the homology of this bifiltration, we introduce two closely related combinatorial bifiltrations, one polyhedral and the other simplicial, which are both topologically equivalent to the multicover bifiltration and far smaller than a Čech-based model considered in prior work of Sheehy.

The olfactory limbus of the red fox (). New insights regarding a noncanonical olfactory bulb pathway.

The olfactory system in most mammals is divided into several subsystems based on the anatomical locations of the neuroreceptor cells involved and the receptor families that are expressed. In addition to the main olfactory system and the vomeronasal system, a range of olfactory subsystems converge onto the transition zone located between the main olfactory bulb (MOB) and the accessory olfactory bulb (AOB), which has been termed the olfactory limbus (OL). The OL contains specialized glomeruli that receive noncanonical sensory afferences and which interact with the MOB and AOB.

A Simple Algorithm for Higher-Order Delaunay Mosaics and Alpha Shapes.

We present a simple algorithm for computing higher-order Delaunay mosaics that works in Euclidean spaces of any finite dimensions. The algorithm selects the vertices of the order- mosaic from incrementally constructed lower-order mosaics and uses an algorithm for weighted first-order Delaunay mosaics as a black-box to construct the order- mosaic from its vertices. Beyond this black-box, the algorithm uses only combinatorial operations, thus facilitating easy implementation.

Using gridCoal to assess whether standard population genetic theory holds in the presence of spatio-temporal heterogeneity in population size.

Spatially explicit population genetic models have long been developed, yet have rarely been used to test hypotheses about the spatial distribution of genetic diversity or the genetic divergence between populations. Here, we use spatially explicit coalescence simulations to explore the properties of the island and the two-dimensional stepping stone models under a wide range of scenarios with spatio-temporal variation in deme size. We avoid the simulation of genetic data, using the fact that under the studied models, summary statistics of genetic diversity and divergence can be approximated from coalescence times.

Theory of Chirality Induced Spin Selectivity: Progress and Challenges.

A critical overview of the theory of the chirality-induced spin selectivity (CISS) effect, that is, phenomena in which the chirality of molecular species imparts significant spin selectivity to various electron processes, is provided. Based on discussions in a recently held workshop, and further work published since, the status of CISS effects-in electron transmission, electron transport, and chemical reactions-is reviewed. For each, a detailed discussion of the state-of-the-art in theoretical understanding is provided and remaining challenges and research opportunities are identified.

Early queen infection shapes developmental dynamics and induces long-term disease protection in incipient ant colonies.

Infections early in life can have enduring effects on an organism's development and immunity. In this study, we show that this equally applies to developing 'superorganisms'--incipient social insect colonies. When we exposed newly mated Lasius niger ant queens to a low pathogen dose, their colonies grew more slowly than controls before winter, but reached similar sizes afterwards.

Anderson Localization of Composite Particles.

We investigate the effect of coupling between translational and internal degrees of freedom of composite quantum particles on their localization in a random potential. We show that entanglement between the two degrees of freedom weakens localization due to the upper bound imposed on the inverse participation ratio by purity of a quantum state. We perform numerical calculations for a two-particle system bound by a harmonic force in a 1D disordered lattice and a rigid rotor in a 2D disordered lattice.

Transsynaptic modulation of presynaptic short-term plasticity in hippocampal mossy fiber synapses.

The hippocampal mossy fiber synapse is a key synapse of the trisynaptic circuit. Post-tetanic potentiation (PTP) is the most powerful form of plasticity at this synaptic connection. It is widely believed that mossy fiber PTP is an entirely presynaptic phenomenon, implying that PTP induction is input-specific, and requires neither activity of multiple inputs nor stimulation of postsynaptic neurons.

Subcellular patch-clamp techniques for single-bouton stimulation and simultaneous pre- and postsynaptic recording at cortical synapses.

Rigorous investigation of synaptic transmission requires analysis of unitary synaptic events by simultaneous recording from presynaptic terminals and postsynaptic target neurons. However, this has been achieved at only a limited number of model synapses, including the squid giant synapse and the mammalian calyx of Held. Cortical presynaptic terminals have been largely inaccessible to direct presynaptic recording, due to their small size.

Two linked loci under mutation-selection balance and Muller's ratchet.

We report complete analysis of a deterministic model of deleterious mutations and negative selection against them at two haploid loci without recombination. As long as mutation is a weaker force than selection, mutant alleles remain rare at the only stable equilibrium, and otherwise, a variety of dynamics are possible. If the mutation-free genotype is absent, generally the only stable equilibrium is the one that corresponds to fixation of the mutant allele at the locus where it is less deleterious.

A step in the Delaunay mosaic of order .

Given a locally finite set and an integer , we consider the function on the dual of the order- Voronoi tessellation, whose sublevel sets generalize the notion of alpha shapes from order-1 to order- (Edelsbrunner et al. in IEEE Trans Inf Theory IT-29:551-559, 1983; Krasnoshchekov and Polishchuk in Inf Process Lett 114:76-83, 2014). While this function is not necessarily generalized discrete Morse, in the sense of Forman (Adv Math 134:90-145, 1998) and Freij (Discrete Math 309:3821-3829, 2009), we prove that it satisfies similar properties so that its increments can be meaningfully classified into critical and non-critical steps.

Mechanism of mediated alkali peroxide oxidation and triplet versus singlet oxygen formation.

Aprotic alkali metal-O batteries face two major obstacles to their chemistry occurring efficiently, the insulating nature of the formed alkali superoxides/peroxides and parasitic reactions that are caused by the highly reactive singlet oxygen (O). Redox mediators are recognized to be key for improving rechargeability. However, it is unclear how they affect O formation, which hinders strategies for their improvement.

MOD: A novel machine-learning optimal-filtering method for accurate and efficient detection of subthreshold synaptic events in vivo.

Background: To understand information coding in single neurons, it is necessary to analyze subthreshold synaptic events, action potentials (APs), and their interrelation in different behavioral states. However, detecting excitatory postsynaptic potentials (EPSPs) or currents (EPSCs) in behaving animals remains challenging, because of unfavorable signal-to-noise ratio, high frequency, fluctuating amplitude, and variable time course of synaptic events.

New Method: We developed a method for synaptic event detection, termed MOD (Machine-learning Optimal-filtering Detection-procedure), which combines concepts of supervised machine learning and optimal Wiener filtering.

Molecular Impurities as a Realization of Anyons on the Two-Sphere.

Studies on the experimental realization of two-dimensional anyons in terms of quasiparticles have been restricted, so far, to only anyons on the plane. It is known, however, that the geometry and topology of space can have significant effects on quantum statistics for particles moving on it. Here, we have undertaken the first step toward realizing the emerging fractional statistics for particles restricted to move on the sphere instead of on the plane.

Integration of spatial and non-spatial information by heterogeneous dentate gyrus granule cells.

The hippocampus is the key site for learning and memory and for processing of spatial information in the brain. It is divided into three main subregions: the dentate gyrus (DG), the CA3 area, and the CA1 region, which are linearly interconnected to form a so-called trisynaptic circuit. Thus, the DG sits in a strategic position to gate the flow of information from the neocortex into the hippocampal network.

Coupling of hippocampal theta and ripples with pontogeniculooccipital waves.

The hippocampus has a major role in encoding and consolidating long-term memories, and undergoes plastic changes during sleep. These changes require precise homeostatic control by subcortical neuromodulatory structures. The underlying mechanisms of this phenomenon, however, remain unknown.

Author Correction: Persistent and reversible solid iodine electrodeposition in nanoporous carbons.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Persistent and reversible solid iodine electrodeposition in nanoporous carbons.

Aqueous iodine based electrochemical energy storage is considered a potential candidate to improve sustainability and performance of current battery and supercapacitor technology. It harnesses the redox activity of iodide, iodine, and polyiodide species in the confined geometry of nanoporous carbon electrodes. However, current descriptions of the electrochemical reaction mechanism to interconvert these species are elusive.

Selective Routing of Spatial Information Flow from Input to Output in Hippocampal Granule Cells.

Dentate gyrus granule cells (GCs) connect the entorhinal cortex to the hippocampal CA3 region, but how they process spatial information remains enigmatic. To examine the role of GCs in spatial coding, we measured excitatory postsynaptic potentials (EPSPs) and action potentials (APs) in head-fixed mice running on a linear belt. Intracellular recording from morphologically identified GCs revealed that most cells were active, but activity level varied over a wide range.

Analytic Model of Chiral-Induced Spin Selectivity.

Organic materials are known to feature long spin-diffusion times, originating in a generally small spin-orbit coupling observed in these systems. From that perspective, chiral molecules acting as efficient spin selectors pose a puzzle that attracted a lot of attention in recent years. Here, we revisit the physical origins of chiral-induced spin selectivity (CISS) and propose a simple analytic minimal model to describe it.