Pegasos: primal estimated sub-gradient solver for SVM

We describe and analyze a simple and effective stochastic sub-gradient descent algorithm for solving the optimization problem cast by Support Vector Machines (SVM). We prove that the number of iterations required to obtain a solution of accuracy e{\epsilon} is [(O)\tilde](1 / e){\tilde{O}(1 / \epsilon)}, where each iteration operates on a single training example. In contrast, previous analyses of stochastic gradient descent methods for SVMs require W(1 / e²){\Omega(1 / \epsilon^2)} iterations. As in previously devised SVM solvers, the number of iterations also scales linearly with 1/λ, where λ is the regularization parameter of SVM. For a linear kernel, the total run-time of our method is [(O)\tilde](d/(le)){\tilde{O}(d/(\lambda \epsilon))}, where d is a bound on the number of non-zero features in each example. Since the run-time does not depend directly on the size of the training set, the resulting algorithm is especially suited for learning from large datasets. Our approach also extends to non-linear kernels while working solely on the primal objective function, though in this case the runtime does depend linearly on the training set size. Our algorithm is particularly well suited for large text classification problems, where we demonstrate an order-of-magnitude speedup over previous SVM learning methods.     

Two-Parameter Lévy Processes Along Decreasing Paths

Let {X_t1,t2:t₁,t₂ 3 0}\{X_{t_{1},t_{2}}:t_{1},t_{2}\geq0\} be a two-parameter Lévy process on ℝ ^d . We study basic properties of the one-parameter process {X _x(t),y(t):t∈T} where x and y are, respectively, nondecreasing and nonincreasing nonnegative continuous functions on the interval T. We focus on and characterize the case where the process has stationary increments.     

W-Band pulse EPR distance measurements in peptides using Gd(3+)-dipicolinic acid derivatives as spin labels

We present high field DEER (double electron-electron resonance) distance measurements using Gd(3+) (S = 7/2) spin labels for probing peptides' conformations in solution. The motivation for using Gd(3+) spin labels as an alternative for the standard nitroxide spin labels is the sensitivity improvement they offer because of their very intense EPR signal at high magnetic fields. Gd(3+) was coordinated by dipicolinic acid derivative (4MMDPA) tags that were covalently attached to two cysteine thiol groups. Cysteines were introduced in positions 15 and 27 of the peptide melittin and then two types of spin labeled melittins were prepared, one labeled with two nitroxide spin labels and the other with two 4MMDPA-Gd(3+) labels. Both types were subjected to W-band (95 GHz, 3.5 T) DEER measurements. For the Gd(3+) labeled peptide we explored the effect of the solution molar ratio of Gd(3+) and the labeled peptide, the temperature, and the maximum dipolar evolution time T on the DEER modulation depth. We found that the optimization of the [Gd(3+)]/[Tag] ratio is crucial because excess Gd(3+) masked the DEER effect and too little Gd(3+) resulted in the formation of Gd(3+)-tag(2) complexes, generating peptide dimers. In addition, we observed that the DEER modulation depth is sensitive to spectral diffusion processes even at Gd(3+) concentrations as low as 0.2 mM and therefore experimental conditions should be chosen to minimize it as it decreases the DEER effect. Finally, the distance between the two Gd(3+) ions, 3.4 nm, was found to be longer by 1.2 nm than the distance between the two nitroxides. The origin and implications of this difference are discussed.     

Control of the Structure and Functions of Biomaterials by Light

Vision and other light-triggered biochemical transformations in plants and living organisms represent a sophisticated biological processes in which optical signals are recorded and transduced as (physico)chemical events. Photoswitchable biomaterials are a new class of substances in which optical signals generate discrete “On” and “Off” states of biological functions, resembling logic gates that flip between 0 and 1 states in response to the changes in electric currents in computers. The (photo)chemistry of photochromic materials has been extensively developed in the past four decades. These materials isomerize reversibly upon light absorption, and the discrete photoisomeric states exhibit distinct spectral and chemical features. Integration of photoisomerizable (or photochromic) units into biomaterials allow their secondary functions such as biocatalysis, binding, and electron transfer to be tailored so that they can be switched on or off. This can be accomplished by chemical modification of the biomaterial by photoisomerizable units and by integration of biomaterials in photoisomerizable microenvironments such as monolayers or polymers. The photoswitchable properties of chemically modified biomaterials originate from the light-induced generation or perturbation of the biologically active site, whereas in photoisomerizable matrices they depend upon the regulation of the physical or chemical features of the photoisomerizable assemblies of polymers, monolayers, or membranes. Light-triggered activation of catalytic biomaterials provides a means of amplifying the recorded optical signal by biochemical transformations, and photostimulated biochemical redox switches allow its electrochemical transduction and amplification. The field of photoswitches based on biomaterials has developed extensively in the past few years within the general context of molecular switching devices and micromachinery. The extensive knowledge on the manipulation of biomaterials through genetic engineering and the fabrication of surfaces modified by biologically active materials enables us to prepare biomaterials with improved optical-switching features. Their application in optoelectronic or bioelectronic devices has been transformed from fantasy to reality. The use of photoswitchable biomaterials in information storage and processing devices (biocomputers), sensors, reversible immunosensors, and biological amplifiers of optical signals has already been demonstrated, but still leaves important future challenges.     

Identification of G‐nerve agents at picogram levels from complex organic samples containing hydrocarbon interferences by aqueous extraction,followed by derivatization and liquid chromatography‐mass spectrometry analysis

The chromatograms obtained from the gas chromatography‐electron ionization mass spectrometric (GC‐EI‐MS) analysis of extracts containing G‐nerve agents in the presence of diesel, gasoline, etc., are dominated by hydrocarbon backgrounds that “mask” the G‐nerve agents, leading to severe difficulties in identification. This paper presents a practical solution for this challenge by transferring the G‐nerve agents from the organic phase into the aqueous phase using liquid‐liquid extraction (LLE), followed by derivatization with 2‐[(dimethylamino)methyl]phenol (2‐DMAMP), allowing ultrasensitive LC‐ESI‐MS/MS analysis of the G‐derivatives. The proposed approach enables rapid identification of trace amounts of G‐nerve agents with limits of identification (LOIs) at the pg/mL scale.