Molecular pathways controlling the sequential steps of cortical projection neuron migration - Hippenmeyer, Simon (Cellular and Molecular Control of Neuronal Migration)
Coordinated migration of newly-born neurons to their target territories is essential for correct neuronal circuit assembly in the developing brain. Although a cohort of signaling pathways has been implicated in the regulation of cortical projection neuron migration, the precise molecular mechanisms and how a balanced interplay of cell-autonomous and non-autonomous functions of candidate signaling molecules controls the discrete steps in the migration process, are just being revealed. In this chapter, I will focally review recent advances that improved our understanding of the cell-autonomous and possible cell-nonautonomous functions of the evolutionarily conserved LIS1/NDEL1-complex in regulating the sequential steps of cortical projection neuron migration. I will then elaborate on the emerging concept that the Reelin signaling pathway, acts exactly at precise stages in the course of cortical projection neuron migration. Lastly, I will discuss how finely tuned transcriptional programs and downstream effectors govern particular aspects in driving radial migration at discrete stages and how they regulate the precise positioning of cortical projection neurons in the developing cerebral cortex.

Partial enumeration and curvature regularization - Olsson, Carl; Ulen, Johannes; Boykov, Yuri; Kolmogorov, Vladimir
Energies with high-order non-submodular interactions have been shown to be very useful in vision due to their high modeling power. Optimization of such energies, however, is generally NP-hard. A naive approach that works for small problem instances is exhaustive search, that is, enumeration of all possible labelings of the underlying graph. We propose a general minimization approach for large graphs based on enumeration of labelings of certain small patches. This partial enumeration technique reduces complex high-order energy formulations to pairwise Constraint Satisfaction Problems with unary costs (uCSP), which can be efficiently solved using standard methods like TRW-S. Our approach outperforms a number of existing state-of-the-art algorithms on well known difficult problems (e.g. curvature regularization, stereo, deconvolution); it gives near global minimum and better speed. Our main application of interest is curvature regularization. In the context of segmentation, our partial enumeration technique allows to evaluate curvature directly on small patches using a novel integral geometry approach.

On the mass concentration for Bose-Einstein condensates with attractive interactions - Guo, Yujin; Seiringer, Robert (Letters in Mathematical Physics)
We consider two-dimensional Bose-Einstein condensates with attractive interaction, described by the Gross-Pitaevskii functional. Minimizers of this functional exist only if the interaction strength a satisfies Mathematical expression, where Q is the unique positive radial solution of Mathematical expression in Mathematical expression. We present a detailed analysis of the behavior of minimizers as a approaches a*, where all the mass concentrates at a global minimum of the trapping potential.

Morpho-physiological criteria divide dentate gyrus interneurons into classes - Hosp, Jonas; Strüber, Michael; Yanagawa, Yuchio; Obata, Kunihiko; Vida, Imre; Jonas, Peter M; Bartos, Marlene (Hippocampus)
GABAergic inhibitory interneurons control fundamental aspects of neuronal network function. Their functional roles are assumed to be defined by the identity of their input synapses, the architecture of their dendritic tree, the passive and active membrane properties and finally the nature of their postsynaptic targets. Indeed, interneurons display a high degree of morphological and physiological heterogeneity. However, whether their morphological and physiological characteristics are correlated and whether interneuron diversity can be described by a continuum of GABAergic cell types or by distinct classes has remained unclear. Here we perform a detailed morphological and physiological characterization of GABAergic cells in the dentate gyrus, the input region of the hippocampus. To achieve an unbiased and efficient sampling and classification we used knock-in mice expressing the enhanced green fluorescent protein (eGFP) in glutamate decarboxylase 67 (GAD67)-positive neurons and performed cluster analysis. We identified five interneuron classes, each of them characterized by a distinct set of anatomical and physiological parameters. Cross-correlation analysis further revealed a direct relation between morphological and physiological properties indicating that dentate gyrus interneurons fall into functionally distinct classes which may differentially control neuronal network activity.

Equivalence of two definitions of the effective mass of a polaron - Lieb, Élliott; Seiringer, Robert (Journal of Statistical Physics)
Two definitions of the effective mass of a particle interacting with a quantum field, such as a polaron, are considered and shown to be equal in models similar to the Fröhlich polaron model. These are: 1. the mass defined by the low momentum energy E(P)≈E(0)+P2/2 M of the translation invariant system constrained to have momentum P and 2. the mass M of a simple particle in an arbitrary slowly varying external potential, V, described by the nonrelativistic Schrödinger equation, whose ground state energy equals that of the combined particle/field system in a bound state in the same V.

Rational points on pencils of conics and quadrics with many degenerate fibres - Timothy Browning; Matthiesen, Lilian; Skorobogatov, Alexei N (Annals of Mathematics)
For any pencil of conics or higher-dimensional quadrics over ℚ, with all degenerate fibres defined over ℚ, we show that the Brauer–Manin obstruction controls weak approximation. The proof is based on the Hasse principle and weak approximation for some special intersections of quadrics over ℚ, which is a consequence of recent advances in additive combinatorics.

Cubic hypersurfaces and a version of the circle method for number fields - Timothy Browning; Vishe, Pankaj (Duke Mathematical Journal)
A version of the Hardy-Littlewood circle method is developed for number fields K/ℚ and is used to show that nonsingular projective cubic hypersurfaces over K always have a K-rational point when they have dimension at least 8.

Counting rational points on del Pezzo surfaces with a conic bundle structure - Timothy Browning; Jones, Michael S (Acta Arithmetica)
For any number field k, upper bounds are established for the number of k-rational points of bounded height on non-singular del Pezzo surfaces defined over k, which are equipped with suitable conic bundle structures over k.

The polynomial sieve and equal sums of like polynomials - Browning, Timothy D (International Mathematics Research Notices)
A new "polynomial sieve" is presented and used to show that almost all integers have at most one representation as a sum of two values of a given polynomial of degree at least 3.

Rational points on intersections of cubic and quadric hypersurfaces - Browning, Timothy D; Dietmann, Rainer; Heath Brown, Roger (Journal of the Institute of Mathematics of Jussieu)
We investigate the Hasse principle for complete intersections cut out by a quadric hypersurface and a cubic hypersurface defined over the rational numbers.

Edit propagation using geometric relationship functions - Guerrero, Paul; Jeschke, Stefan; Wimmer, Michael; Wonka, Peter (ACM Transactions on Graphics)
We propose a method for propagating edit operations in 2D vector graphics, based on geometric relationship functions. These functions quantify the geometric relationship of a point to a polygon, such as the distance to the boundary or the direction to the closest corner vertex. The level sets of the relationship functions describe points with the same relationship to a polygon. For a given query point, we first determine a set of relationships to local features, construct all level sets for these relationships, and accumulate them. The maxima of the resulting distribution are points with similar geometric relationships. We show extensions to handle mirror symmetries, and discuss the use of relationship functions as local coordinate systems. Our method can be applied, for example, to interactive floorplan editing, and it is especially useful for large layouts, where individual edits would be cumbersome. We demonstrate populating 2D layouts with tens to hundreds of objects by propagating relatively few edit operations.

Constrained Verifiable Random Functions - Fuchsbauer, Georg (SCN 2014)
We extend the notion of verifiable random functions (VRF) to constrained VRFs, which generalize the concept of constrained pseudorandom functions, put forward by Boneh and Waters (Asiacrypt’13), and independently by Kiayias et al. (CCS’13) and Boyle et al. (PKC’14), who call them delegatable PRFs and functional PRFs, respectively. In a standard VRF the secret key sk allows one to evaluate a pseudorandom function at any point of its domain; in addition, it enables computation of a non-interactive proof that the function value was computed correctly. In a constrained VRF from the key sk one can derive constrained keys skS for subsets S of the domain, which allow computation of function values and proofs only at points in S. After formally defining constrained VRFs, we derive instantiations from the multilinear-maps-based constrained PRFs by Boneh and Waters, yielding a VRF with constrained keys for any set that can be decided by a polynomial-size circuit. Our VRFs have the same function values as the Boneh-Waters PRFs and are proved secure under the same hardness assumption, showing that verifiability comes at no cost. Constrained (functional) VRFs were stated as an open problem by Boyle et al.

Generalised interpolation by solving recursion free-horn clauses - Gupta, Ashutosh; Popeea, Corneliu; Rybalchenko, Andrey (Electronic Proceedings in Theoretical Computer Science, EPTCS)
In this paper we present INTERHORN, a solver for recursion-free Horn clauses. The main application domain of INTERHORN lies in solving interpolation problems arising in software verification. We show how a range of interpolation problems, including path, transition, nested, state/transition and well-founded interpolation can be handled directly by INTERHORN. By detailing these interpolation problems and their Horn clause representations, we hope to encourage the emergence of a common back-end interpolation interface useful for diverse verification tools.

Spatio-temporal representations of uncertainty in spiking neural networks - Savin, Cristina; Denève, Sophie
It has been long argued that, because of inherent ambiguity and noise, the brain needs to represent uncertainty in the form of probability distributions. The neural encoding of such distributions remains however highly controversial. Here we present a novel circuit model for representing multidimensional real-valued distributions using a spike based spatio-temporal code. Our model combines the computational advantages of the currently competing models for probabilistic codes and exhibits realistic neural responses along a variety of classic measures. Furthermore, the model highlights the challenges associated with interpreting neural activity in relation to behavioral uncertainty and points to alternative population-level approaches for the experimental validation of distributed representations.

Interface simulation distances - Cerny, Pavol; Chmelik, Martin; Henzinger, Thomas A; Radhakrishna, Arjun (Theoretical Computer Science)
The classical (boolean) notion of refinement for behavioral interfaces of system components is the alternating refinement preorder. In this paper, we define a distance for interfaces, called interface simulation distance. It makes the alternating refinement preorder quantitative by, intuitively, tolerating errors (while counting them) in the alternating simulation game. We show that the interface simulation distance satisfies the triangle inequality, that the distance between two interfaces does not increase under parallel composition with a third interface, that the distance between two interfaces can be bounded from above and below by distances between abstractions of the two interfaces, and how to synthesize an interface from incompatible requirements. We illustrate the framework, and the properties of the distances under composition of interfaces, with two case studies.

PtSi clustering in silicon probed by transport spectroscopy - Mongillo, Massimo; Spathis, Panayotis N; Georgios Katsaros; De Franceschi, Silvano; Gentile, Pascal; Rurali, Riccardo; Cartoixà, Xavier (Physical Review X)
Metal silicides formed by means of thermal annealing processes are employed as contact materials in microelectronics. Control of the structure of silicide/silicon interfaces becomes a critical issue when the characteristic size of the device is reduced below a few tens of nanometers. Here, we report on silicide clustering occurring within the channel of PtSi/Si/PtSi Schottky-barrier transistors. This phenomenon is investigated through atomistic simulations and low-temperature resonant-tunneling spectroscopy. Our results provide evidence for the segregation of a PtSi cluster with a diameter of a few nanometers from the silicide contact. The cluster acts as a metallic quantum dot giving rise to distinct signatures of quantum transport through its discrete energy states.

Dynamic task allocation in asynchronous shared memory - Alistarh, Dan-Adrian; Aspnes, James; Bender, Michael; Gelashvili, Rati; Gilbert, Seth
Task allocation is a classic distributed problem in which a set of p potentially faulty processes must cooperate to perform a set of tasks. This paper considers a new dynamic version of the problem, in which tasks are injected adversarially during an asynchronous execution. We give the first asynchronous shared-memory algorithm for dynamic task allocation, and we prove that our solution is optimal within logarithmic factors. The main algorithmic idea is a randomized concurrent data structure called a dynamic to-do tree, which allows processes to pick new tasks to perform at random from the set of available tasks, and to insert tasks at random empty locations in the data structure. Our analysis shows that these properties avoid duplicating work unnecessarily. On the other hand, since the adversary controls the input as well the scheduling, it can induce executions where lots of processes contend for a few available tasks, which is inefficient. However, we prove that every algorithm has the same problem: given an arbitrary input, if OPT is the worst-case complexity of the optimal algorithm on that input, then the expected work complexity of our algorithm on the same input is O(OPT log3 m), where m is an upper bound on the number of tasks that are present in the system at any given time.

Tight bounds for asynchronous renaming - Alistarh, Dan-Adrian; Aspnes, James; Censor Hillel, Keren; Gilbert, Seth; Guerraoui, Rachid (Journal of the ACM)
This article presents the first tight bounds on the time complexity of shared-memory renaming, a fundamental problem in distributed computing in which a set of processes need to pick distinct identifiers from a small namespace. We first prove an individual lower bound of ω(k) process steps for deterministic renaming into any namespace of size subexponential in k, where k is the number of participants. The bound is tight: it draws an exponential separation between deterministic and randomized solutions, and implies new tight bounds for deterministic concurrent fetch-and-increment counters, queues, and stacks. The proof is based on a new reduction from renaming to another fundamental problem in distributed computing: mutual exclusion. We complement this individual bound with a global lower bound of ω(klog(k/c)) on the total step complexity of renaming into a namespace of size ck, for any c = 1. This result applies to randomized algorithms against a strong adversary, and helps derive new global lower bounds for randomized approximate counter implementations, that are tight within logarithmic factors. On the algorithmic side, we give a protocol that transforms any sorting network into a randomized strong adaptive renaming algorithm, with expected cost equal to the depth of the sorting network. This gives a tight adaptive renaming algorithm with expected step complexity O(log k), where k is the contention in the current execution. This algorithm is the first to achieve sublinear time, and it is time-optimal as per our randomized lower bound. Finally, we use this renaming protocol to build monotone-consistent counters with logarithmic step complexity and linearizable fetch-and-increment registers with polylogarithmic cost.

StackTrack: An automated transactional approach to concurrent memory reclamation - Alistarh, Dan-Adrian; Eugster, Patrick; Herlihy, Maurice; Matveev, Alexander; Shavit, Nir
Dynamic memory reclamation is arguably the biggest open problem in concurrent data structure design: All known solutions induce high overhead, or must be customized to the specific data structure by the programmer, or both. This paper presents StackTrack, the first concurrent memory reclamation scheme that can be applied automatically by a compiler, while maintaining efficiency. StackTrack eliminates most of the expensive bookkeeping required for memory reclamation by leveraging the power of hardware transactional memory (HTM) in a new way: it tracks thread variables dynamically, and in an atomic fashion. This effectively makes all memory references visible without having threads pay the overhead of writing out this information. Our empirical results show that this new approach matches or outperforms prior, non-automated, techniques.

Balls-into-Leaves: Sub-logarithmic renaming in synchronous message-passing systems - Alistarh, Dan-Adrian; Denysyuk, Oksana; Rodrígues, Luís; Shavit, Nir
We consider the following natural problem: n failure-prone servers, communicating synchronously through message passing, must assign themselves one-to-one to n distinct items. Existing literature suggests two possible approaches to this problem. First, model it as an instance of tight renaming in synchronous message-passing systems; for deterministic solutions, a tight bound of ©(logn) communication rounds is known. Second, model the scenario as an instance of randomized load-balancing, for which elegant sub-logarithmic solutions exist. However, careful examination reveals that known load-balancing schemes do not apply to our scenario, because they either do not tolerate faults or do not ensure one-to-one allocation. It is thus natural to ask if sublogarithmic solutions exist for this apparently simple but intriguing problem. In this paper, we combine the two approaches to provide a new randomized solution for tight renaming, which terminates in O (log log n) communication rounds with high probability, against a strong adaptive adversary. Our solution, called Balls-into-Leaves, combines the deterministic approach with a new randomized scheme to obtain perfectly balanced allocations. The algorithm arranges the items as leaves of a tree, and participants repeatedly perform random choices among the leaves. The algorithm exchanges information in each round to split the participants into progressively smaller groups whose random choices do not conflict. We then extend the algorithm to terminate early in O(log log) rounds w.h.p., where is the actual number of failures. These results imply an exponential separation between deterministic and randomized algorithms for the tight renaming problem in message-passing systems.