Convex analysis for minimizing and learning submodular set functions

The connections between convexity and submodularity are explored, for purposes of minimizing and learning submodular set functions.

First, we develop a novel method for minimizing a particular class of submodular functions, which can be expressed as a sum of concave functions composed with modular functions. The basic algorithm uses an accelerated first order method applied to a smoothed version of its convex extension. The smoothing algorithm is particularly novel as it allows us to treat general concave potentials without needing to construct a piecewise linear approximation as with graph-based techniques.

Second, we derive the general conditions under which it is possible to find a minimizer of a submodular function via a convex problem. This provides a framework for developing submodular minimization algorithms. The framework is then used to develop several algorithms that can be run in a distributed fashion. This is particularly useful for applications where the submodular objective function consists of a sum of many terms, each term dependent on a small part of a large data set.

Lastly, we approach the problem of learning set functions from an unorthodox perspective---sparse reconstruction. We demonstrate an explicit connection between the problem of learning set functions from random evaluations and that of sparse signals. Based on the observation that the Fourier transform for set functions satisfies exactly the conditions needed for sparse reconstruction algorithms to work, we examine some different function classes under which uniform reconstruction is possible.

Vorlesungen über die Theorie der elliptischen Modulfunctionen,

Available on demand as hard copy or computer file from Cornell University Library.

Les fonctions polyédriques et modulaires.

Available on demand as hard copy or computer file from Cornell University Library.

A Gag peptide encompassing B- and T-cell epitopes of the caprine arthritis encephalitis virus functions as modular carrier peptide

Short synthetic peptides are important tools in biomedical research permitting to generate hapten specific polyclonal sera for analytical purposes or functional studies. In this paper we provide proof of principle that a peptide located in a highly conserved portion of the Gag protein of the caprine arthritis encephalitis virus and carrying an immunodominant T helper cell epitope functions as an efficient carrier peptide, mediating a strong antibody response to a peptidic hapten encompassing a well-characterized B cell epitope of Env. The carrier and hapten peptides were collinearly synthesized permutating their molecular arrangement. While the antibody response to the hapten was similar for both constructs, the antibody response to a B cell epitope overlapping the T helper cell epitope of the Gag carrier peptide was considerably different. This permits a modular use of the carrier peptide to generate antibody directed exclusively to the hapten peptide or a strong humoral response to both carrier- and hapten-peptide. Finally, we have mapped the epitopes involved in this polarized antibody response and discussed the potential immunological implications.

Cryptographic hash functions

Cryptographic hash functions are an important tool of cryptography and play a fundamental role in efficient and secure information processing. A hash function processes an arbitrary finite length input message to a fixed length output referred to as the hash value. As a security requirement, a hash value should not serve as an image for two distinct input messages and it should be difficult to find the input message from a given hash value. Secure hash functions serve data integrity, non-repudiation and authenticity of the source in conjunction with the digital signature schemes. Keyed hash functions, also called message authentication codes (MACs) serve data integrity and data origin authentication in the secret key setting. The building blocks of hash functions can be designed using block ciphers, modular arithmetic or from scratch. The design principles of the popular Merkle–Damgård construction are followed in almost all widely used standard hash functions such as MD5 and SHA-1.

PRUNE and PROBE-two modular web services for protein-protein docking

The protein-protein docking programs typically perform four major tasks: (i) generation of docking poses, (ii) selecting a subset of poses, (iii) their structural refinement and (iv) scoring, ranking for the final assessment of the true quaternary structure. Although the tasks can be integrated or performed in a serial order, they are by nature modular, allowing an opportunity to substitute one algorithm with another. We have implemented two modular web services, (i) PRUNE: to select a subset of docking poses generated during sampling search (http://pallab.serc.iisc.ernet.in/prune) and (ii) PROBE: to refine, score and rank them (http://pallab.serc.iisc.ernet.in/probe). The former uses a new interface area based edge-scoring function to eliminate > 95% of the poses generated during docking search. In contrast to other multi-parameter-based screening functions, this single parameter based elimination reduces the computational time significantly, in addition to increasing the chances of selecting native-like models in the top rank list. The PROBE server performs ranking of pruned poses, after structure refinement and scoring using a regression model for geometric compatibility, and normalized interaction energy. While web-service similar to PROBE is infrequent, no web-service akin to PRUNE has been described before. Both the servers are publicly accessible and free for use.

Typical and atypical domain combinations in human protein kinases: functions, disease causing mutations and conservation in other primates

Ser/Thr and Tyr protein kinases orchestrate many signalling pathways and hence loss in this balance leads to many disease phenotypes. Due to their high abundance, diversity and importance, efforts have been made in the past to classify kinases and annotate their functions at both gross and fine levels. These kinases are conventionally classified into subfamilies based on the sequences of catalytic domains. Usually the domain architecture of a full-length kinase is consistent with the subfamily classification made based on the sequence of kinase domain. Important contributions of modular domains to the overall function of the kinase are well known. Recently occurrence of two kinds of outlier kinases-''Hybrid'' and ``Rogue'' has been reported. These show considerable deviations in their domain architectures from the typical domain architecture known for the classical kinase subfamilies. This article provides an overview of the different subfamilies of human kinases and the role of non-kinase domains in functions and diseases. Importantly this article provides analysis of hybrid and rogue kinases encoded in the human genome and highlights their conservation in closely related primate species. These kinases are examples of elegant rewiring to bring about subtle functional differences compared to canonical variants.

A Scalable and Programmable Modular Traffic Manager Architecture

A key issue in the design of next generation Internet routers and switches will be provision of traffic manager (TM) functionality in the datapaths of their high speed switching fabrics. A new architecture that allows dynamic deployment of different TM functions is presented. By considering the processing requirements of operations such as policing and congestion, queuing, shaping and scheduling, a solution has been derived that is scalable with a consistent programmable interface. Programmability is achieved using a function computation unit which determines the action (e.g. drop, queue, remark, forward) based on the packet attribute information and a memory storage part. Results of a Xilinx Virtex-5 FPGA reference design are presented.

Central-Tapped Node Linked Modular Fault-Tolerance Topology for SRM Applications

Electric vehicles (EVs) and hybrid electric vehicles (HEVs) can reduce greenhouse gas emissions while switched reluctance motor (SRM) is one of the promising motor for such applications. This paper presents a novel SRM fault-diagnosis and fault-tolerance operation solution. Based on the traditional asymmetric half-bridge topology for the SRM driving, the central tapped winding of the SRM in modular half-bridge configuration are introduced to provide fault-diagnosis and fault-tolerance functions, which are set idle in normal conditions. The fault diagnosis can be achieved by detecting the characteristic of the excitation and demagnetization currents. An SRM fault-tolerance operation strategy is also realized by the proposed topology, which compensates for the missing phase torque under the open-circuit fault, and reduces the unbalanced phase current under the short-circuit fault due to the uncontrolled faulty phase. Furthermore, the current sensor placement strategy is also discussed to give two placement methods for low cost or modular structure. Simulation results in MATLAB/Simulink and experiments on a 750-W SRM validate the effectiveness of the proposed strategy, which may have significant implications and improve the reliability of EVs/HEVs.

PP1 interactomes as a means of characterizing protein functions

A maioria das funções celulares, incluindo expressão de genes, crescimento e proliferação celulares, metabolismo, morfologia, motilidade, comunicação intercelular e apoptose, é regulada por interações proteína-proteína (IPP). A célula responde a uma variedade de estímulos, como tal a expressão de proteínas é um processo dinâmico e os complexos formados são constituídos transitoriamente mudando de acordo com o seu ciclo funcional, adicionalmente, muitas proteínas são expressas de uma forma dependente do tipo de célula. Em qualquer instante a célula pode conter cerca de centenas de milhares de IPPs binárias, e encontrar os companheiros de interação de uma proteína é um meio de inferir a sua função. Alterações em redes de IPP podem também fornecer informações acerca de mecanismos de doença. O método de identificação binário mais frequentemente usado é o sistema Dois Hibrido de Levedura, adaptado para rastreio em larga escala. Esta metodologia foi aqui usada para identificar os interactomas específicos de isoforma da Proteína Fosfatase 1 (PP1), em cérebro humano. A PP1 é uma proteína fosfatase de Ser/Thr envolvida numa grande variedade de vias e eventos celulares. É uma proteína conservada codificada por três genes, que originam as isoformas α, β, e γ, com a última a originar γ1 e γ2 por splicing alternativo. As diferentes isoformas da PP1 são reguladas pelos companheiros de interação – proteínas que interagem com a PP1 (PIPs). A natureza modular dos complexos da PP1, bem como a sua associação combinacional, gera um largo reportório de complexos reguladores e papéis em circuitos de sinalização celular. Os interactomas da PP1 específicos de isofoma, em cérebro, foram aqui descritos, com um total de 263 interações identificadas e integradas com os dados recolhidos de várias bases de dados de IPPs. Adicionalmente, duas PIPs foram selecionadas para uma caracterização mais aprofundada da interação: Taperina e Sinfilina-1A. A Taperina é uma proteína ainda pouco descrita, descoberta recentemente como sendo uma PIP. A sua interação com as diferentes isoformas da PP1 e localização celulares foram analisadas. Foi descoberto que a Taperina é clivada e que está presente no citoplasma, membrana e núcleo e que aumenta os níveis de PP1, em células HeLa. Na membrana ela co-localiza com a PP1 e a actina e uma forma mutada da Taperina, no motivo de ligação à PP1, está enriquecida no núcleo, juntamente com a actina. Mais, foi descoberto que a Taperina é expressa em testículo e localiza-se na região acrossómica da cabeça do espermatozoide, uma estrutura onde a PP1 e a actina estão também presentes. A Sinfilina-1A, uma isoforma da Sinfilina-1, é uma proteína com tendência para agregar e tóxica, envolvida na doença de Parkinson. Foi mostrado que a Sinfilina-1A liga às isoformas da PP1, por co-transformação em levedura, e que mutação do seu motivo de ligação à PP1 diminuiu significativamente a interação, num ensaio de overlay. Quando sobre-expressa em células Cos-7, a Sinfilina-1A formou corpos de inclusão onde a PP1 estava presente, no entanto a forma mutada da Sinfilina-1A também foi capaz de agregar, indicando que a formação de inclusões não foi dependente de ligação à PP1. Este trabalho dá uma nova perspetiva dos interactomas da PP1, incluindo a identificação de dezenas de companheiros de ligação específicos de isoforma, e enfatiza a importância das PIPs, não apenas na compreensão das funções celulares da PP1 mas também, como alvos de intervenção terapêutica.

Efficient subwindow search with submodular score functions

Subwindow search aims to find the optimal subimage which maximizes the score function of an object to be detected. After the development of the branch and bound (B&B) method called Efficient Subwindow Search (ESS), several algorithms (IESS [2], AESS [2], ARCS [3]) have been proposed to improve the performance of ESS. For nn images, IESS's time complexity is bounded by O(n³) which is better than ESS, but only applicable to linear score functions. Other work shows that Monge properties can hold in subwindow search and can be used to speed up the search to O(n³), but only applies to certain types of score functions. In this paper we explore the connection between submodular functions and the Monge property, and prove that sub-modular score functions can be used to achieve O(n³) time complexity for object detection. The time complexity can be further improved to be sub-cubic by applying B&B methods on row interval only, when the score function has a multivariate submodular bound function. Conditions for sub-modularity of common non-linear score functions and multivariate submodularity of their bound functions are also provided, and experiments are provided to compare the proposed approach against ESS and ARCS for object detection with some nonlinear score functions.

Numerical Computation of a Certain Dirichlet Series Attached to Siegel Modular Forms of Degree Two

The Rankin convolution type Dirichlet series D-F,D-G(s) of Siegel modular forms F and G of degree two, which was introduced by Kohnen and the second author, is computed numerically for various F and G. In particular, we prove that the series D-F,D-G(s), which shares the same functional equation and analytic behavior with the spinor L-functions of eigenforms of the same weight are not linear combinations of those. In order to conduct these experiments a numerical method to compute the Petersson scalar products of Jacobi Forms is developed and discussed in detail.

Desarrollo de un sistema hardware modular que implemente los instrumentos de un laboratorio de electrónica

El poder disponer de la instrumentación y los equipos electrónicos resulta vital en el diseño de circuitos analógicos. Permiten realizar las pruebas necesarias y el estudio para el buen funcionamiento de estos circuitos. Los equipos se pueden diferenciar en instrumentos de excitación, los que proporcionan las señales al circuito, y en instrumentos de medida, los que miden las señales generadas por el circuito. Estos equipos sirven de gran ayuda pero a su vez tienen un precio elevado lo que impide en muchos casos disponer de ellos. Por esta principal desventaja, se hace necesario conseguir un dispositivo de bajo coste que sustituya de alguna manera a los equipos reales. Si el instrumento es de medida, este sistema de bajo coste puede ser implementado mediante un equipo hardware encargado de adquirir los datos y una aplicación ejecutándose en un ordenador donde analizarlos y presentarlos en la pantalla. En el caso de que el instrumento sea de excitación, el único cometido del sistema hardware es el de proporcionar las señales cuya configuración ha enviado el ordenador. En un equipo real, es el propio equipo el que debe realizar todas esas acciones: adquisición, procesamiento y presentación de los datos. Además, la dificultad de realizar modificaciones o ampliaciones de las funcionalidades en un instrumento tradicional con respecto a una aplicación de queda patente. Debido a que un instrumento tradicional es un sistema cerrado y uno cuya configuración o procesamiento de datos es hecho por una aplicación, algunas de las modificaciones serían realizables modificando simplemente el software del programa de control, por lo que el coste de las modificaciones sería menor. En este proyecto se pretende implementar un sistema hardware que tenga las características y realice las funciones del equipamiento real que se pueda encontrar en un laboratorio de electrónica. También el desarrollo de una aplicación encargada del control y el análisis de las señales adquiridas, cuya interfaz gráfica se asemeje a la de los equipos reales para facilitar su uso. ABSTRACT. The instrumentation and electronic equipment are vital for the design of analogue circuits. They enable to perform the necessary testing and study for the proper functioning of these circuits. The devices can be classified into the following categories: excitation instruments, which transmit the signals to the circuit, and measuring instruments, those in charge of measuring the signals produced by the circuit. This equipment is considerably helpful, however, its high price often makes it hardly accessible. For this reason, low price equipment is needed in order to replace real devices. If the instrument is measuring, this low cost system can be implemented by hardware equipment to acquire the data and running on a computer where analyzing and present on the screen application. In case of an excitation the instrument, the only task of the hardware system is to provide signals which sent the computer configuration. In a real instrument, is the instrument itself that must perform all these actions: acquisition, processing and presentation of data. Moreover, the difficulty of making changes or additions to the features in traditional devices with respect to an application running on a computer is evident. This is due to the fact that a traditional instrument is a closed system and its configuration or data processing is made by an application. Therefore, certain changes can be made just by modifying the control program software. Consequently, the cost of these modifications is lower. This project aims to implement a hardware system with the same features and functions of any real device, available in an electronics laboratory. Besides, it aims to develop an application for the monitoring and analysis of acquired signals. This application is provided with a graphic interface resembling those of real devices in order to facilitate its use.

Modular organization of the Friend murine leukemia virus envelope protein underlies the mechanism of infection

Retrovirus infection is initiated by receptor-dependent fusion of the envelope to the cell membrane. The modular organization of the envelope protein of C type retroviruses has been exploited to investigate how binding of the surface subunit (SU) to receptor triggers fusion mediated by the transmembrane (TM) subunit. We show that deletion of the receptor-binding domain (RBD) from SU of Friend murine leukemia virus (Fr-MLV) abolishes infection that is restored by supplying RBD as a soluble protein. Infection by this mechanism remains dependent on receptor expression. When membrane attachment of the virus lacking RBD is reestablished by inserting the hormone erythropoietin, infection remains dependent on the RBD/receptor complex. However, infection increases 50-fold to 5 × 105 units/ml on cells that also express the erythropoietin receptor. Soluble RBD from Fr-MLV also restores infection by amphotropic and xenotropic MLVs in which RBD is deleted. These experiments demonstrate that RBD has two functions: mediating virus attachment and activating the fusion mechanism. In addition, they indicate that receptor engagement triggers fusion by promoting a subgroup-independent functional interaction between RBD and the remainder of SU and/or TM.

SMART, a simple modular architecture research tool: Identification of signaling domains

Accurate multiple alignments of 86 domains that occur in signaling proteins have been constructed and used to provide a Web-based tool (SMART: simple modular architecture research tool) that allows rapid identification and annotation of signaling domain sequences. The majority of signaling proteins are multidomain in character with a considerable variety of domain combinations known. Comparison with established databases showed that 25% of our domain set could not be deduced from SwissProt and 41% could not be annotated by Pfam. SMART is able to determine the modular architectures of single sequences or genomes; application to the entire yeast genome revealed that at least 6.7% of its genes contain one or more signaling domains, approximately 350 greater than previously annotated. The process of constructing SMART predicted (i) novel domain homologues in unexpected locations such as band 4.1-homologous domains in focal adhesion kinases; (ii) previously unknown domain families, including a citron-homology domain; (iii) putative functions of domain families after identification of additional family members, for example, a ubiquitin-binding role for ubiquitin-associated domains (UBA); (iv) cellular roles for proteins, such predicted DEATH domains in netrin receptors further implicating these molecules in axonal guidance; (v) signaling domains in known disease genes such as SPRY domains in both marenostrin/pyrin and Midline 1; (vi) domains in unexpected phylogenetic contexts such as diacylglycerol kinase homologues in yeast and bacteria; and (vii) likely protein misclassifications exemplified by a predicted pleckstrin homology domain in a Candida albicans protein, previously described as an integrin.