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A single layer ferromagnetic film magnetized in the plane of an ac current flow, exhibits a characteristic Hall voltage with harmonic and second harmonic components, which is attributed to the presence of spin currents with polarization non-collinear with the magnetization. A set of 30 nm thick permalloy (Py) films used in this study are deposited at an oblique angle with respect to the substrate plane which induces an in-plane easy axis in the magnetization of the initial nucleating layers of the films which is distinct from the overall bulk magnetic properties of the film. This unusual magnetic texture provides a platform for the direct detection of inverse spin Hall effect in Hall bar shaped macroscopic devices at room temperatures which we denote as Anomalous Inverse Spin Hall Effect (AISHE). Control samples fabricated by normal deposition of permalloy with slow rotation of substrate shows significant reduction of the harmonic Hall signal that further substantiates the model. The analysis of the second harmonic Hall signal corroborates the presence of spin-orbit torque arising from the unconventional spin-currents in the single-layer ferromagnets.

The phenomenon of Spin Hall Effect (SHE) generates a pure spin current transverse to an applied current in materials with strong spin-orbit coupling, although not detectable through conventional electrical measurement. An intuitive Hall effect like measurement configuration is implemented to directly measure pure spin chemical potential of the accumulated spins at the edges of heavy metal (HM) channels that generates large SHE. A pair of transverse linearly aligned voltage probes in placed in ohmic contact with the top surface of HM , one being a ferromagnetic metal (FM) with non-zero spin polarization and other is the reference metal (RM) with zero polarization of carriers. This combination of FM/RM electrodes is shown to induce an additional voltage proportional to a spin accumulation potential, which is anti symmetric with respect to opposite orientations of FM controlled by a 2D vector magnet. Proof of concept of the measurement scheme is verified by comparing the signs of voltages for HM channels of Tungsten (W) and Platinum (Pt) which are known to generate opposite spin accumulation under similar conditions of applied current. The same devices are also able to detect the reciprocal effect, inverse spin Hall effect (ISHE) by swapping the current and voltage leads and the results are consistent with reciprocity principle. Further, exploiting a characteristic feature of W thin film deposition, a series of devices were fabricated with W resistivity varying over a wide range of 10 - 750 $\mu \Omega$-cm and the calculated spin Hall resistivity exhibits a pronounced power law dependence on resistivity. Our measurement scheme combined with almost two decades of HM resistivity variation provides the ideal platform required to test the underlying microscopic mechanism responsible for SHE/ISHE.

We studied longitudinal and Hall photothermal voltages under a planar magnetic field scan in epitaxial thin films of the Topological Insulator (TI) Sb2Te3, grown using pulsed laser deposition (PLD). Unlike prior research that utilised polarised light-induced photocurrent to investigate the TI, our study introduces advancements based on unpolarized light-induced local heating. This method yields a thermoelectric response exhibiting a direct signature of strong spin-orbit coupling. Our analysis reveals three distinct contributions when fitting the photothermal voltage data to the angular dependence of the planar magnetic field. The interaction between the applied magnetic field and the thermal gradient on the bulk band orbitals enables the differentiation between the ordinary Nernst effect from the out-of-plane thermal gradient and an extraordinary magneto-thermal contribution from the planar thermal gradient. The fitting of our data to theoretical models indicates that these effects primarily arise from the bulk states of the TI rather than the surface states. These findings highlight PLD-grown epitaxial topological insulator thin films as promising candidates for optoelectronic devices, including sensors and actuators. Such devices offer controllable responses through position-dependent, non-invasive local heating via focused incident light and variations in the applied magnetic field direction.

Utilizing the spin-induced pumping from a ferromagnet (FM) into a heavy metal (HM) under the ferromagnetic resonance (FMR) condition, we report an enhancement in effective damping in $\beta$- W/Py bilayers by systematically varying resistivity ($\rho_{W}$) of $\beta$-W films. Different resistivity ranging from 100 $\mu\Omega$-cm to 1400 $\mu\Omega$-cm with a thickness of 8 nm can be achieved by varying the argon pressure ($P_{Ar}$) during the growth by the method of sputtering. The coefficient of effective damping $\alpha_{eff}$ is observed to increase from 0.010 to 0.025 with $\rho_{W}$, which can be modulated by $P_{Ar}$. We observe a modest dependence of $\alpha_{eff}$ on the sputtering power ($p_{S}$) while keeping the $P_{Ar}$ constant. $\alpha_{eff}$ dependence on both $P_{Ar}$ and $p_{S}$ suggests that there exists a strong correlation between $\alpha_{eff}$ and $\rho_{W}$. It is thus possible to utilize $\rho_{W}$ as a tuning parameter to regulate the $\alpha_{eff}$, which can be advantageous for faster magnetization dynamics switching. The thickness dependence study of Py in the aforementioned bilayers manifests a higher spin mixing conductance ($g^{\uparrow\downarrow}_{eff}$) which suggests a strong spin pumping from Py into the $\beta$-W layer. The effective spin current ($J_{S(eff)}$) is also evaluated by considering the spin-back flow in this process. Intrinsic spin mixing conductance ($g^{\uparrow\downarrow}_{W}$) and spin diffusion length ($\lambda_{SD}$) of $\beta$-W are additionally investigated using thickness variations in $\beta$-W. Furthermore, the low-temperature study in $\beta$-W/Py reveals an intriguing temperature dependence in $\alpha_{eff}$ which is quite different from $\alpha_{b}$ of single Py layer and the enhancement in $\alpha_{eff}$ at low temperature can be attributed to the spin-induced pumping from Py layer into $\beta$-W.

Neodymium nickelate, NdNiO3 attracts attraction due to the simultaneous occurrence of several phase transitions around the same temperature. The electronic properties of NdNiO3 are extremely complex as structural distortion, electron correlation, charge ordering, and orbital overlapping play significant roles in the transitions. We report the effects of electron and hole injection via doping a single 3d metal, V, in the NdNiO3 nanostructures to understand the variations in the electronic properties without any structural distortion. A reversible resistivity modulation more than five orders of magnitude via hole doping and complete suppression of metal to insulator transition via electron doping is observed along with the switching of major charge carriers. The modulation of electronic properties without any structural distortion and external strain opens up new directions to consider the NdNi1_xVxO3 nanostructures applicable as emerging electronic devices.

Contemporary Artificial Intelligence (AI) stands on two legs: large training data corpora and many-parameter artificial neural networks (ANNs). The data corpora are needed to represent the complexity and heterogeneity of the world. The role of the networks is less transparent due to the obscure dependence of the network parameters and outputs on the training data and inputs. This raises problems, ranging from technical-scientific to legal-ethical. We hypothesize that a transparent approach to machine learning is possible without using networks at all. By generalizing a parameter-free, statistically consistent data interpolation method, which we analyze theoretically in detail, we develop a network-free framework for AI incorporating generative modeling. We demonstrate this framework with examples from three different disciplines - ethology, control theory, and mathematics. Our generative Hilbert framework applied to the trajectories of small groups of swimming fish outperformed state-of-the-art traditional mathematical behavioral models and current ANN-based models. We demonstrate pure data interpolation based control by stabilizing an inverted pendulum and a driven logistic map around unstable fixed points. Finally, we present a mathematical application by predicting zeros of the Riemann Zeta function, achieving comparable performance as a transformer network. We do not suggest that the proposed framework will always outperform networks as over-parameterized networks can interpolate. However, our framework is theoretically sound, transparent, deterministic, and parameter free: remarkably, it does not require any compute-expensive training, does not involve optimization, has no model selection, and is easily reproduced and ported. We also propose an easily computed method of credit assignment based on this framework, to help address ethical-legal challenges raised by generative AI., Comment: 47 pages with 8 figures + 33 pages supplementary with 7 figures and one table (total 80 pages)

Textbook wisdom advocates for smooth function fits and implies that interpolation of noisy data should lead to poor generalization. A related heuristic is that fitting parameters should be fewer than measurements (Occam's Razor). Surprisingly, contemporary machine learning (ML) approaches, cf. deep nets (DNNs), generalize well despite interpolating noisy data. This may be understood via Statistically Consistent Interpolation (SCI), i.e. data interpolation techniques that generalize optimally for big data. In this article we elucidate SCI using the weighted interpolating nearest neighbors (wiNN) algorithm, which adds singular weight functions to kNN (k-nearest neighbors). This shows that data interpolation can be a valid ML strategy for big data. SCI clarifies the relation between two ways of modeling natural phenomena: the rationalist approach (strong priors) of theoretical physics with few parameters and the empiricist (weak priors) approach of modern ML with more parameters than data. SCI shows that the purely empirical approach can successfully predict. However data interpolation does not provide theoretical insights, and the training data requirements may be prohibitive. Complex animal brains are between these extremes, with many parameters, but modest training data, and with prior structure encoded in species-specific mesoscale circuitry. Thus, modern ML provides a distinct epistemological approach different both from physical theories and animal brains.

Neuroscientific data analysis has traditionally relied on linear algebra and stochastic process theory. However, the tree-like shapes of neurons cannot be described easily as points in a vector space (the subtraction of two neuronal shapes is not a meaningful operation), and methods from computational topology are better suited to their analysis. Here we introduce methods from Discrete Morse (DM) Theory to extract the tree-skeletons of individual neurons from volumetric brain image data, and to summarize collections of neurons labelled by tracer injections. Since individual neurons are topologically trees, it is sensible to summarize the collection of neurons using a consensus tree-shape that provides a richer information summary than the traditional regional 'connectivity matrix' approach. The conceptually elegant DM approach lacks hand-tuned parameters and captures global properties of the data as opposed to previous approaches which are inherently local. For individual skeletonization of sparsely labelled neurons we obtain substantial performance gains over state-of-the-art non-topological methods (over 10% improvements in precision and faster proofreading). The consensus-tree summary of tracer injections incorporates the regional connectivity matrix information, but in addition captures the collective collateral branching patterns of the set of neurons connected to the injection site, and provides a bridge between single-neuron morphology and tracer-injection data., Comment: 20 pages (14 pages main-text and 6 pages supplementary information). 5 main-text figures. 5 supplementary figures. 2 supplementary tables

Traditionally in regression one minimizes the number of fitting parameters or uses smoothing/regularization to trade training (TE) and generalization error (GE). Driving TE to zero by increasing fitting degrees of freedom (dof) is expected to increase GE. However modern big-data approaches, including deep nets, seem to over-parametrize and send TE to zero (data interpolation) without impacting GE. Overparametrization has the benefit that global minima of the empirical loss function proliferate and become easier to find. These phenomena have drawn theoretical attention. Regression and classification algorithms have been shown that interpolate data but also generalize optimally. An interesting related phenomenon has been noted: the existence of non-monotonic risk curves, with a peak in GE with increasing dof. It was suggested that this peak separates a classical regime from a modern regime where over-parametrization improves performance. Similar over-fitting peaks were reported previously (statistical physics approach to learning) and attributed to increased fitting model flexibility. We introduce a generative and fitting model pair ("Misparametrized Sparse Regression" or MiSpaR) and show that the overfitting peak can be dissociated from the point at which the fitting function gains enough dof's to match the data generative model and thus provides good generalization. This complicates the interpretation of overfitting peaks as separating a "classical" from a "modern" regime. Data interpolation itself cannot guarantee good generalization: we need to study the interpolation with different penalty terms. We present analytical formulae for GE curves for MiSpaR with $l_2$ and $l_1$ penalties, in the interpolating limit $\lambda\rightarrow 0$.These risk curves exhibit important differences and help elucidate the underlying phenomena., Comment: 15 pages, 4 figures

We design a self size-estimating feed-forward network (SSFN) using a joint optimization approach for estimation of number of layers, number of nodes and learning of weight matrices. The learning algorithm has a low computational complexity, preferably within few minutes using a laptop. In addition the algorithm has a limited need for human intervention to tune parameters. SSFN grows from a small-size network to a large-size network, guaranteeing a monotonically non-increasing cost with addition of nodes and layers. The learning approach uses judicious a combination of `lossless flow property' of some activation functions, convex optimization and instance of random matrix. Consistent performance -- low variation across Monte-Carlo trials -- is found for inference performance (classification accuracy) and estimation of network size.

Fano resonance exhibiting an asymmetric spectral line shape is a universal phenomenon observed in diverse physical systems. Here we experimentally establish a direct link between the spectral asymmetry parameter and a physically realizable phase factor of interference between a continuum and a discrete mode that leads to Fano resonance. Using a specially designed metamaterial, namely waveguided plasmonic crystal with a spatially varying orientation axis of plasmonic grating, we demonstrate control on the spectral asymmetry of the Fano resonance through changes in the geometric phase of polarized light. In this scenario, the changes in the geometric phase for input left, and right circular polarized light arises due to varying orientation angle of the grating axis. The systematic changes in the geometric phase and the resulting q-parameter of Fano resonance is interpreted by an appropriate theoretical model connecting the two physical entities. The demonstrated control over the spectral line shape of Fano resonance achieved by tailoring geometric phase may open up novel routes for polarization-based photonic applications.

Anatomy is undergoing a renaissance driven by availability of large digital data sets generated by light microscopy. A central computational task is to map individual data volumes to standardized templates. This is accomplished by regularized estimation of a diffeomorphic transformation between the coordinate systems of the individual data and the template, building the transformation incrementally by integrating a smooth flow field. The canonical volume form of this transformation is used to quantify local growth, atrophy, or cell density. While multiple implementations exist for this estimation, less attention has been paid to the variance of the estimated diffeomorphism for noisy data. Notably, there is an infinite dimensional un-observable space defined by those diffeomorphisms which leave the template invariant. These form the stabilizer subgroup of the diffeomorphic group acting on the template. The corresponding flat directions in the energy landscape are expected to lead to increased estimation variance. Here we show that a least-action principle used to generate geodesics in the space of diffeomorphisms connecting the subject brain to the template removes the stabilizer. This provides reduced-variance estimates of the volume form. Using simulations we demonstrate that the asymmetric large deformation diffeomorphic mapping methods (LDDMM), which explicitly incorporate the asymmetry between idealized template images and noisy empirical images, provide lower variance estimators than their symmetrized counterparts (cf. ANTs). We derive Cramer-Rao bounds for the variances in the limit of small deformations. Analytical results are shown for the Jacobian in terms of perturbations of the vector fields and divergence of the vector field.

Many modern machine learning models are trained to achieve zero or near-zero training error in order to obtain near-optimal (but non-zero) test error. This phenomenon of strong generalization performance for "overfitted" / interpolated classifiers appears to be ubiquitous in high-dimensional data, having been observed in deep networks, kernel machines, boosting and random forests. Their performance is consistently robust even when the data contain large amounts of label noise. Very little theory is available to explain these observations. The vast majority of theoretical analyses of generalization allows for interpolation only when there is little or no label noise. This paper takes a step toward a theoretical foundation for interpolated classifiers by analyzing local interpolating schemes, including geometric simplicial interpolation algorithm and singularly weighted $k$-nearest neighbor schemes. Consistency or near-consistency is proved for these schemes in classification and regression problems. Moreover, the nearest neighbor schemes exhibit optimal rates under some standard statistical assumptions. Finally, this paper suggests a way to explain the phenomenon of adversarial examples, which are seemingly ubiquitous in modern machine learning, and also discusses some connections to kernel machines and random forests in the interpolated regime.

Neuroscientific data analysis has classically involved methods for statistical signal and image processing, drawing on linear algebra and stochastic process theory. However, digitized neuroanatomical data sets containing labelled neurons, either individually or in groups labelled by tracer injections, do not fully fit into this classical framework. The tree-like shapes of neurons cannot mathematically be adequately described as points in a vector space. There is therefore a need for new approaches. Methods from computational topology and geometry are naturally suited to the analysis of neuronal shapes. Here we introduce methods from Discrete Morse Theory to extract tree-skeletons of individual neurons from volumetric brain image data, or to summarize collections of neurons labelled by localized anterograde tracer injections. Since individual neurons are topologically trees, it is sensible to summarize the collection of neurons labelled by a localized anterograde tracer injection using a consensus tree-shape. The algorithmic procedure includes an initial pre-processing step to extract a density field from the raw volumetric image data, followed by initial skeleton extraction from the density field using a discrete version of a 1-(un)stable manifold of the density field. Heuristically, if the density field is regarded as a mountainous landscape, then the 1-(un)stable manifold follows the "mountain ridges" connecting the maxima of the density field. We then simplify this skeleton-graph into a tree using a shortest-path approach and methods derived from persistent homology. The advantage of this approach is that it uses global information about the density field and is therefore robust to local fluctuations and non-uniformly distributed input signals. To be able to handle large data sets, we use a divide-and-conquer approach. The resulting software DiMorSC is available on Github.

Whole brain neuroanatomy using tera-voxel light-microscopic data sets is of much current interest. A fundamental problem in this field is the mapping of individual brain data sets to a reference space. Previous work has not rigorously quantified the distortions in brain geometry from in-vivo to ex-vivo brains due to the tissue processing, which will be important when computing properties such as local cell and process densities at the voxel level in creating reference brain maps. Further, existing approaches focus on registering uni-modal volumetric data; however, given the increasing interest in the marmoset model for neuroscience research, it is necessary to cross-register multi-modal data sets including MRIs and multiple histological series that can help address individual variations in brain architecture. Here we present a computational approach for same-subject multimodal MRI guided reconstruction of a histological series, jointly with diffeomorphic mapping to a reference atlas. We quantify the scale change during the different stages of histological processing of the brains using the Jacobian determinant of the diffeomorphic transformations involved. There are two major steps in the histology process with associated scale distortions (a) brain perfusion (b) histological sectioning and reassembly. By mapping the final image stacks to the ex-vivo post fixation MRI, we show that tape-transfer histology can be reassembled accurately into 3D volumes with a local scale change of 2.0 $\pm$ 0.4% per axis dimension. In contrast, the perfusion step, as assessed by mapping the in-vivo MRIs to the ex-vivo post fixation MRIs, shows a larger local scale change of 6.9 $\pm$ 2.1% per axis dimension. This is the first systematic quantification of the local metric distortions associated with whole-brain histological processing, and we expect that the results will generalize to other species.

We consider a distributed learning setup where a sparse signal is estimated over a network. Our main interest is to save communication resource for information exchange over the network and reduce processing time. Each node of the network uses a convex optimization based algorithm that provides a locally optimum solution for that node. The nodes exchange their signal estimates over the network in order to refine their local estimates. At a node, the optimization algorithm is based on an $\ell_1$-norm minimization with appropriate modifications to promote sparsity as well as to include influence of estimates from neighboring nodes. Our expectation is that local estimates in each node improve fast and converge, resulting in a limited demand for communication of estimates between nodes and reducing the processing time. We provide restricted-isometry-property (RIP)-based theoretical analysis on estimation quality. In the scenario of clean observation, it is shown that the local estimates converge to the exact sparse signal under certain technical conditions. Simulation results show that the proposed algorithms show competitive performance compared to a globally optimum distributed LASSO algorithm in the sense of convergence speed and estimation error.

Modern supervised learning techniques, particularly those using deep nets, involve fitting high dimensional labelled data sets with functions containing very large numbers of parameters. Much of this work is empirical. Interesting phenomena have been observed that require theoretical explanations; however the non-convexity of the loss functions complicates the analysis. Recently it has been proposed that the success of these techniques rests partly in the effectiveness of the simple stochastic gradient descent algorithm in the so called interpolation limit in which all labels are fit perfectly. This analysis is made possible since the SGD algorithm reduces to a stochastic linear system near the interpolating minimum of the loss function. Here we exploit this insight by presenting and analyzing a new distributed algorithm for gradient descent, also in the interpolating limit. The distributed SGD algorithm presented in the paper corresponds to gradient descent applied to a simple penalized distributed loss function, $L({\bf w}_1,...,{\bf w}_n) = \Sigma_i l_i({\bf w}_i) + \mu \sum_{}|{\bf w}_i-{\bf w}_j|^2$. Here each node holds only one sample, and its own parameter vector. The notation $$ denotes edges of a connected graph defining the links between nodes. It is shown that this distributed algorithm converges linearly (ie the error reduces exponentially with iteration number), with a rate $1-\frac{\eta}{n}\lambda_{min}(H)

This paper presents a variational framework for dense diffeomorphic atlas-mapping onto high-throughput histology stacks at the 20 um meso-scale. The observed sections are modelled as Gaussian random fields conditioned on a sequence of unknown section by section rigid motions and unknown diffeomorphic transformation of a three-dimensional atlas. To regularize over the high-dimensionality of our parameter space (which is a product space of the rigid motion dimensions and the diffeomorphism dimensions), the histology stacks are modelled as arising from a first order Sobolev space smoothness prior. We show that the joint maximum a-posteriori, penalized-likelihood estimator of our high dimensional parameter space emerges as a joint optimization interleaving rigid motion estimation for histology restacking and large deformation diffeomorphic metric mapping to atlas coordinates. We show that joint optimization in this parameter space solves the classical curvature non-identifiability of the histology stacking problem. The algorithms are demonstrated on a collection of whole-brain histological image stacks from the Mouse Brain Architecture Project.

We develop an algorithm for systematic design of a large artificial neural network using a progression property. We find that some non-linear functions, such as the rectifier linear unit and its derivatives, hold the property. The systematic design addresses the choice of network size and regularization of parameters. The number of nodes and layers in network increases in progression with the objective of consistently reducing an appropriate cost. Each layer is optimized at a time, where appropriate parameters are learned using convex optimization. Regularization parameters for convex optimization do not need a significant manual effort for tuning. We also use random instances for some weight matrices, and that helps to reduce the number of parameters we learn. The developed network is expected to show good generalization power due to appropriate regularization and use of random weights in the layers. This expectation is verified by extensive experiments for classification and regression problems, using standard databases.

We study fundamental performance limitations of distributed feedback control in large-scale networked dynamical systems. Specifically, we address the question of whether dynamic feedback controllers perform better than static (memoryless) ones when subject to locality constraints. We consider distributed linear consensus and vehicular formation control problems modeled over toric lattice networks. For the resulting spatially invariant systems we study the large-scale asymptotics (in network size) of global performance metrics that quantify the level of network coherence. With static feedback from relative state measurements, such metrics are known to scale unfavorably in lattices of low spatial dimensions, preventing, for example, a 1-dimensional string of vehicles to move like a rigid object. We show that the same limitations in general apply also to dynamic feedback control that is locally of first order. This means that the addition of one local state to the controller gives a similar asymptotic performance to the memoryless case. This holds unless the controller can access noiseless measurements of its local state with respect to an absolute reference frame, in which case the addition of controller memory may fundamentally improve performance. In simulations of platoons with 20-200 vehicles we show that the performance limitations we derive manifest as unwanted accordion-like motions. Similar behaviors are to be expected in any network that is embeddable in a low-dimensional toric lattice, and the same fundamental limitations would apply. To derive our results, we present a general technical framework for the analysis of stability and performance of spatially invariant systems in the limit of large networks., Comment: To appear in IEEE Transactions on Automatic Control, 2019. First submitted October 2017. This version February 2019

We investigate an existing distributed algorithm for learning sparse signals or data over networks. The algorithm is iterative and exchanges intermediate estimates of a sparse signal over a network. This learning strategy using exchange of intermediate estimates over the network requires a limited communication overhead for information transmission. Our objective in this article is to show that the strategy is good for learning in spite of limited communication. In pursuit of this objective, we first provide a restricted isometry property (RIP)-based theoretical analysis on convergence of the iterative algorithm. Then, using simulations, we show that the algorithm provides competitive performance in learning sparse signals vis-a-vis an existing alternate distributed algorithm. The alternate distributed algorithm exchanges more information including observations and system parameters.

While modern imaging technologies such as fMRI have opened exciting new possibilities for studying the brain in vivo, histological sections remain the best way to study the anatomy of the brain at the level of single neurons. The histological atlas changed little since 1909 and localizing brain regions is a still a labor intensive process performed only by experienced neuro-anatomists. Existing digital atlases such as the Allen Brain atlas are limited to low resolution images which cannot identify the detailed structure of the neurons. We have developed a digital atlas methodology that combines information about the 3D organization of the brain and the detailed texture of neurons in different structures. Using the methodology we developed an atlas for the mouse brainstem and mid-brain, two regions for which there are currently no good atlases. Our atlas is "active" in that it can be used to automatically align a histological stack to the atlas, thus reducing the work of the neuroanatomist., Comment: 8 pages, 10 figures, appeared in proceeding of MICCAI 2017

Contemporary technological challenges often involve many degrees of freedom in a distributed or networked setting. Three aspects are notable: the variables are usually associated with the nodes of a graph with limited communication resources, hindering centralized control; the communication is subjected to noise; and the number of variables can be very large. These three aspects make tools and techniques from statistical physics particularly suitable for the performance analysis of such networked systems in the limit of many variables (analogous to the thermodynamic limit in statistical physics). Perhaps not surprisingly, phase-transition like phenomena appear in these systems, where a sharp change in performance can be observed with a smooth parameter variation, with the change becoming discontinuous or singular in the limit of infinite system size. In this paper we analyze the so called network consensus problem, prototypical of the above considerations, that has been previously analyzed mostly in the context of additive noise. We show that qualitatively new phase-transition like phenomena appear for this problem in the presence of multiplicative noise. Depending on dimensions and on the presence or absence of a conservation law, the system performance shows a discontinuous change at a threshold value of the multiplicative noise strength. In the absence of the conservation law, and for graph spectral dimension less than two, the multiplicative noise threshold (the stability margin of the control problem) is zero. This is reminiscent of the absence of robust controllers for certain classes of centralized control problems. Although our study involves a toy model we believe that the qualitative features are generic, with implication for the robust stability of distributed control systems, as well as the effect of roundoff errors and communication noise on distributed algorithms., Comment: Submitted To JSTATMECH

The next grand challenges for society and science are in the brain sciences. A collection of 60+ scientists from around the world, together with 10+ observers from national, private, and foundations, spent two days together discussing the top challenges that we could solve as a global community in the next decade. We eventually settled on three challenges, spanning anatomy, physiology, and medicine. Addressing all three challenges requires novel computational infrastructure. The group proposed the advent of The International Brain Station (TIBS), to address these challenges, and launch brain sciences to the next level of understanding., Comment: 6 pages

Recovery of an $N$-dimensional, $K$-sparse solution $\mathbf{x}$ from an $M$-dimensional vector of measurements $\mathbf{y}$ for multivariate linear regression can be accomplished by minimizing a suitably penalized least-mean-square cost $||\mathbf{y}-\mathbf{H} \mathbf{x}||_2^2+\lambda V(\mathbf{x})$. Here $\mathbf{H}$ is a known matrix and $V(\mathbf{x})$ is an algorithm-dependent sparsity-inducing penalty. For `random' $\mathbf{H}$, in the limit $\lambda \rightarrow 0$ and $M,N,K\rightarrow \infty$, keeping $\rho=K/N$ and $\alpha=M/N$ fixed, exact recovery is possible for $\alpha$ past a critical value $\alpha_c = \alpha(\rho)$. Assuming $\mathbf{x}$ has iid entries, the critical curve exhibits some universality, in that its shape does not depend on the distribution of $\mathbf{x}$. However, the algorithmic phase transition occurring at $\alpha=\alpha_c$ and associated universality classes remain ill-understood from a statistical physics perspective, i.e. in terms of scaling exponents near the critical curve. In this article, we analyze the mean-field equations for two algorithms, Basis Pursuit ($V(\mathbf{x})=||\mathbf{x}||_{1} $) and Elastic Net ($V(\mathbf{x})= ||\mathbf{x}||_{1} + \tfrac{g}{2} ||\mathbf{x}||_{2}^2$) and show that they belong to different universality classes in the sense of scaling exponents, with Mean Squared Error (MSE) of the recovered vector scaling as $\lambda^\frac{4}{3}$ and $\lambda$ respectively, for small $\lambda$ on the critical line. In the presence of additive noise, we find that, when $\alpha>\alpha_c$, MSE is minimized at a non-zero value for $\lambda$, whereas at $\alpha=\alpha_c$, MSE always increases with $\lambda$., Comment: 18 pages, 8 figures, 3 tables

Penalized regression methods aim to retrieve reliable predictors among a large set of putative ones from a limited amount of measurements. In particular, penalized regression with singular penalty functions is important for sparse reconstruction algorithms. For large-scale problems, these algorithms exhibit sharp phase transition boundaries where sparse retrieval breaks down. Large optimization problems associated with sparse reconstruction have been analyzed in the literature by setting up corresponding statistical mechanical models at a finite temperature. Using replica method for mean field approximation, and subsequently taking a zero temperature limit, this approach reproduces the algorithmic phase transition boundaries. Unfortunately, the replica trick and the non-trivial zero temperature limit obscure the underlying reasons for the failure of a sparse reconstruction algorithm, and of penalized regression methods, in general. In this paper, we employ the ``cavity method'' to give an alternative derivation of the mean field equations, working directly in the zero-temperature limit. This derivation provides insight into the origin of the different terms in the self-consistency conditions. The cavity method naturally involves a quantity, the average local susceptibility, whose behavior distinguishes different phases in this system. This susceptibility can be generalized for analysis of a broader class of sparse reconstruction algorithms., Comment: 15 pages, 7 figures, new version focusing only on cavity method, title change

Stereotactic targeting is a commonly used technique for performing injections in the brains of mice and other animals. The most common method for targeting stereoscopic injections uses the skull indentations bregma and lambda as reference points and is limited in its precision by factors such as skull curvature and individual variation, as well as an incomplete correspondence between skull landmarks and brain locations. In this software tool, a 3D laser scan of the mouse skull is taken in vitro and registered onto a reference skull using a point cloud matching algorithm, and the parameters of the transformation are used to position a glass pipette to place tracer injections. The software was capable of registering sample skulls with less than 100 micron error, and was able to target an injection in a mouse with error of roughly 500 microns. These results indicate that using skull scan registration has the potential to be widely applicable in automating stereotactic targeting of tracer injections., Comment: 8 pages

The voxelized Allen Atlas of the adult mouse brain (at a resolution of 200 microns) has been used in [arXiv:1303.0013] to estimate the region-specificity of 64 cell types whose transcriptional profile in the mouse brain has been measured in microarray experiments. In particular, the model yields estimates for the brain-wide density of each of these cell types. We conduct numerical experiments to estimate the errors in the estimated density profiles. First of all, we check that a simulated thalamic profile based on 200 well-chosen genes can transfer signal from cerebellar Purkinje cells to the thalamus. This inspires us to sub-sample the atlas of genes by repeatedly drawing random sets of 200 genes and refitting the model. This results in a random distribution of density profiles, that can be compared to the predictions of the model. This results in a ranking of cell types by the overlap between the original and sub-sampled density profiles. Cell types with high rank include medium spiny neurons, several samples of cortical pyramidal neurons, hippocampal pyramidal neurons, granule cells and cholinergic neurons from the brain stem. In some cases with lower rank, the average sub-sample can have better contrast properties than the original model (this is the case for amygdalar neurons and dopaminergic neurons from the ventral midbrain). Finally, we add some noise to the cell-type-specific transcriptomes by mixing them using a scalar parameter weighing a random matrix. After refitting the model, we observe than a mixing parameter of $5\%$ leads to modifications of density profiles that span the same interval as the ones resulting from sub-sampling., Comment: 178 pages, 207 figures, 7 tables; v2: typos corrected; v3: more typos corrected, missing pseudo-code in section 3.5 written, image attachment changed in Figure 6, misuse of notation $r^{signal}$ corrected, conclusions unchanged

The Allen Atlas of the adult mouse brain is used to estimate the region-specificity of 64 cell types whose transcriptional profile in the mouse brain has been measured in microarray experiments. We systematically analyze the preliminary results presented in [arXiv:1111.6217], using the techniques implemented in the Brain Gene Expression Analysis toolbox. In particular, for each cell-type-specific sample in the study, we compute a brain-wide correlation profile to the Allen Atlas, and estimate a brain-wide density profile by solving a quadratic optimization problem at each voxel in the mouse brain. We characterize the neuroanatomical properties of the correlation and density profiles by ranking the regions of the left hemisphere delineated in the Allen Reference Atlas. We compare these rankings to prior biological knowledge of the brain region from which the cell-type-specific sample was extracted., Comment: V1: 88 pages, 37 figures, 43 tables; V2: 137 pages, new section discussing different fitting panels

We review quantitative methods and software developed to analyze genome-scale, brain-wide spatially-mapped gene-expression data. We expose new methods based on the underlying high-dimensional geometry of voxel space and gene space, and on simulations of the distribution of co-expression networks of a given size. We apply them to the Allen Atlas of the adult mouse brain, and to the co-expression network of a set of genes related to nicotine addiction retrieved from the NicSNP database. The computational methods are implemented in {\ttfamily{BrainGeneExpressionAnalysis}}, a Matlab toolbox available for download., Comment: 25 pages, 8 figures, accepted in Quantitative Biology (2012) 0002

The Allen Brain Atlas project (ABA) generated a genome-scale collection of gene-expression profiles using in-situ hybridization. These profiles were co-registered to the three-dimensional Allen Reference Atlas (ARA) of the adult mouse brain. A set of more than 4,000 such volumetric data are available for the full brain, at a resolution of 200 microns. These data are presented in a voxel-by-gene matrix. The ARA comes with several systems of annotation, hierarchical (40 cortical regions, 209 sub-cortical regions in the whole brain), or non-hierarchical (12 regions in the left hemisphere, with refinement into 94 regions, and cortical layers). The high-dimensional nature of this dataset and the possible connection between anatomy and gene expression pose challenges to data analysis. We developed the Brain Gene Expression Analysis Toolbox, whose functionalities include: determination of marker genes for brain regions, statistical analysis of brain-wide co-expression patterns, and the computation of brain-wide correlation maps with cell-type specific microarray data., Comment: 59 pages; v2: bug fixed on page 5, preface added; v3: more bugs fixed, cell-type-specific data released (chapter 5); v4: references added, chapter 2 expanded; v5: download link fixed, more typos corrected; v6: download link fixed

We use the Allen Gene Expression Atlas (AGEA) and the OMA ortholog dataset to investigate the evolution of mouse-brain neuroanatomy from the standpoint of the molecular evolution of brain-specific genes. For each such gene, using the phylogenetic tree for all fully sequenced species and the presence of orthologs of the gene in these species, we construct and assign a discrete measure of evolutionary age. The gene expression profile of all gene of similar age, relative to the average gene expression profile, distinguish regions of the brain that are over-represented in the corresponding evolutionary timescale. We argue that the conclusions one can draw on evolution of twelve major brain regions from such a molecular level analysis supplements existing knowledge of mouse brain evolution and introduces new quantitative tools, especially for comparative studies, when AGEA-like data sets for other species become available. Using the functional role of the genes representational of a certain evolutionary timescale and brain region we compare and contrast, wherever possible, our observations with existing knowledge in evolutionary neuroanatomy., Comment: 14 pages

The three-dimensional data-driven Allen Gene Expression Atlas of the adult mouse brain consists of numerized in-situ hybridization data for thousands of genes, co-registered to the Allen Reference Atlas. We propose quantitative criteria to rank genes as markers of a brain region, based on the localization of the gene expression and on its functional fitting to the shape of the region. These criteria lead to natural generalizations to sets of genes. We find sets of genes weighted with coefficients of both signs with almost perfect localization in all major regions of the left hemisphere of the brain, except the pallidum. Generalization of the fitting criterion with positivity constraint provides a lesser improvement of the markers, but requires sparser sets of genes., Comment: 6 pages, 5 figures

We consider distributed consensus and vehicular formation control problems. Specifically we address the question of whether local feedback is sufficient to maintain coherence in large-scale networks subject to stochastic disturbances. We define macroscopic performance measures which are global quantities that capture the notion of coherence; a notion of global order that quantifies how closely the formation resembles a solid object. We consider how these measures scale asymptotically with network size in the topologies of regular lattices in 1, 2 and higher dimensions, with vehicular platoons corresponding to the 1 dimensional case. A common phenomenon appears where a higher spatial dimension implies a more favorable scaling of coherence measures, with a dimensions of 3 being necessary to achieve coherence in consensus and vehicular formations under certain conditions. In particular, we show that it is impossible to have large coherent one dimensional vehicular platoons with only local feedback. We analyze these effects in terms of the underlying energetic modes of motion, showing that they take the form of large temporal and spatial scales resulting in an accordion-like motion of formations. A conclusion can be drawn that in low spatial dimensions, local feedback is unable to regulate large-scale disturbances, but it can in higher spatial dimensions. This phenomenon is distinct from, and unrelated to string instability issues which are commonly encountered in control problems for automated highways., Comment: To appear in IEEE Trans. Automat. Control; 15 pages, 2 figures

Much of the genome is expressed in the vertebrate brain, with individual genes exhibiting different spatially-varying patterns of expression. These variations are not independent, with pairs of genes exhibiting complex patterns of co-expression, such that two genes may be similarly expressed in one region, but differentially expressed in other regions. These correlations have been previously studied quantitatively, particularly for the gene expression atlas of the mouse brain, but the biological meaning of the co-expression patterns remains obscure. We propose a simple model of the co-expression patterns in terms of spatial distributions of underlying cell types. We establish the plausibility of the model in terms of a test set of cell types for which both the gene expression profiles and the spatial distributions are known., Comment: 41 pages; v2: typos corrected

We propose a quantitative method to estimate the statistical properties of sets of genes for which expression data are available and co-registered to a reference atlas of the brain. It is based on graph-theoretic properties of co-expression coefficients between pairs of genes. We apply this method to mouse genes from the Allen Gene Expression Atlas. Co-expression patterns of a list of several hundreds of genes related to addiction are analyzed, using ISH data produced for the mouse brain at the Allen Institute. It appears that large subsets of this set of genes are much more highly co-expressed than expected by chance., Comment: 11 pages, 3 figures; v2: 2 figures added, references added