Some Theorems for Feed Forward Neural Networks

In this paper we introduce a new method which employs the concept of "Orientation Vectors" to train a feed forward neural network and suitable for problems where large dimensions are involved and the clusters are characteristically sparse. The new method is not NP hard as the problem size increases. We `derive' the method by starting from Kolmogrov's method and then relax some of the stringent conditions. We show for most classification problems three layers are sufficient and the network size depends on the number of clusters. We prove as the number of clusters increase from N to N+dN the number of processing elements in the first layer only increases by d(logN), and are proportional to the number of classes, and the method is not NP hard. Many examples are solved to demonstrate that the method of Orientation Vectors requires much less computational effort than Radial Basis Function methods and other techniques wherein distance computations are required, in fact the present method increases logarithmically with problem size compared to the Radial Basis Function method and the other methods which depend on distance computations e.g statistical methods where probabilistic distances are calculated. A practical method of applying the concept of Occum's razor to choose between two architectures which solve the same classification problem has been described. The ramifications of the above findings on the field of Deep Learning have also been briefly investigated and we have found that it directly leads to the existence of certain types of NN architectures which can be used as a "mapping engine", which has the property of "invertibility", thus improving the prospect of their deployment for solving problems involving Deep Learning and hierarchical classification. The latter possibility has a lot of future scope in the areas of machine learning and cloud computing.Comment: 15 pages 13 figure

Detection of Cognitive States from fMRI data using Machine Learning Techniques

Over the past decade functional Magnetic Resonance Imaging (fMRI) has emerged as a powerful technique to locate activity of human brain while engaged in a particular task or cognitive state. We consider the inverse problem of detecting the cognitive state of a human subject based on the fMRI data. We have explored classification techniques such as Gaussian Naive Bayes, k-Nearest Neighbour and Support Vector Machines. In order to reduce the very high dimensional fMRI data, we have used three feature selection strategies. Discriminating features and activity based features were used to select features for the problem of identifying the instantaneous cognitive state given a single fMRI scan and correlation based features were used when fMRI data from a single time interval was given. A case study of visuo-motor sequence learning is presented. The set of cognitive states we are interested in detecting are whether the subject has learnt a sequence, and if the subject is paying attention only towards the position or towards both the color and position of the visual stimuli. We have successfully used correlation based features to detect position-color related cognitive states with 80% accuracy and the cognitive states related to learning with 62.5% accuracy

Using Verbal Autopsy to Measure Causes of Death: the Comparative Performance of Existing Methods.

Monitoring progress with disease and injury reduction in many populations will require widespread use of verbal autopsy (VA). Multiple methods have been developed for assigning cause of death from a VA but their application is restricted by uncertainty about their reliability. We investigated the validity of five automated VA methods for assigning cause of death: InterVA-4, Random Forest (RF), Simplified Symptom Pattern (SSP), Tariff method (Tariff), and King-Lu (KL), in addition to physician review of VA forms (PCVA), based on 12,535 cases from diverse populations for which the true cause of death had been reliably established. For adults, children, neonates and stillbirths, performance was assessed separately for individuals using sensitivity, specificity, Kappa, and chance-corrected concordance (CCC) and for populations using cause specific mortality fraction (CSMF) accuracy, with and without additional diagnostic information from prior contact with health services. A total of 500 train-test splits were used to ensure that results are robust to variation in the underlying cause of death distribution. Three automated diagnostic methods, Tariff, SSP, and RF, but not InterVA-4, performed better than physician review in all age groups, study sites, and for the majority of causes of death studied. For adults, CSMF accuracy ranged from 0.764 to 0.770, compared with 0.680 for PCVA and 0.625 for InterVA; CCC varied from 49.2% to 54.1%, compared with 42.2% for PCVA, and 23.8% for InterVA. For children, CSMF accuracy was 0.783 for Tariff, 0.678 for PCVA, and 0.520 for InterVA; CCC was 52.5% for Tariff, 44.5% for PCVA, and 30.3% for InterVA. For neonates, CSMF accuracy was 0.817 for Tariff, 0.719 for PCVA, and 0.629 for InterVA; CCC varied from 47.3% to 50.3% for the three automated methods, 29.3% for PCVA, and 19.4% for InterVA. The method with the highest sensitivity for a specific cause varied by cause. Physician review of verbal autopsy questionnaires is less accurate than automated methods in determining both individual and population causes of death. Overall, Tariff performs as well or better than other methods and should be widely applied in routine mortality surveillance systems with poor cause of death certification practices

Sodium alginate microspheres containing multicomponent inclusion complex of domperidone

Sodium alginate microspheres of domperidone for intranasal systemic delivery were developed to eliminate first pass metabolism, improve patient compliance and obtain improved therapeutic efficacy in treatment of migraine, gastro-esophageal reflux and chemotherapy induced nausea and vomiting. Domperidone was encapsulated as ternary inclusion complex with β-cyclodextrin and citric acid to improve solubility. The phase solubility studies were performed in order to select suitable acid and ternary inclusion complex was prepared by kneading method. The complex was characterized by differential scanning calorimetry, X-ray diffraction and Fourier transform infrared spectroscopy. In vitro dissolution study was carried out in simulated nasal electrolyte solution, pH 6.4. The microspheres of optimised ternary inclusion complex were prepared by emulsification-cross-linking method and were evaluated for particle size, encapsulation efficiency, equilibrium swelling degree, in vitro mucoadhesion and in vitro drug release. The effect of various formulation variables such as drug loading, polymer concentration, crosslinking agent concentration and cross-linking time on microsphere characteristics were studied. The microspheres size range was 57.63-65.3 µm, whereas the percentage drug encapsulation was within the range 15-50 %. All microspheres showed good bioadhesive properties. The formulation variables influenced the drug release profile. The treatment of in vitro release kinetics with kinetic equations indicated that the domperidone release followed Higuchi's matrix model.Colegio de Farmacéuticos de la Provincia de Buenos Aire

In vitro absorption studies of acyclovir using natural permeation enhancers

Gastroretentive Delivery Systems are employed to improve the bioavailability of drugs which are absorbed through upper part of GIT, by increasing their retention time. Incorporation of permeability enhancers in the formulations of such drugs can further increase their bioavailability; however their use in the formulations is questionable due to the toxicity exhibited by them. Acyclovir is a class III drug having low oral bioavailability due to improper absorption. Mucoadhesive tablets of acyclovir containing natural permeation enhancers were prepared by direct compression and evaluated for mucoadhesion strength, in-vitro dissolution parameters and in-vitro absorption studies. The formulations containing Aloe vera extract showed increase in the mucoadhesion strength and retarded the drug release. The in-vitro absorption studies revealed that the formulations containing Aloe vera extract (Enhancement Ratio 1.94) and chausath prahar pippal (Enhancement Ratio 1.87) showed significant increase in the permeation of the drug. The studies led to the conclusion that by formulating mucoadhesive tablets of acyclovir containing natural permeation enhancers increased the permeability, thus proving to be the cheaper and easily available alternative to the other permeation enhancers.Colegio de Farmacéuticos de la Provincia de Buenos Aire

Local structural changes in paramagnetic and charge ordered phases of Sm0.2Pr0.3Sr0.5MnO3: An EXAFS Study

Sm{0.5-x}Pr{x}Sr{0.5}MnO{3} exhibits variety of ground states as x is varied from 0 to 0.5. At an intermediate doping of x = 0.3 a charge-ordered CE type antiferromagnetic insulating (AFI) ground state is seen. The transition to this ground state is from a paramagnetic insulating (PMI) phase through a ferromagnetic metallic phase (FMM). Local structures in PMI and AFI phases of x = 0.3 sample have been investigated using Pr K-edge and Sm K-edge Extended X-ray Absorption Fine Structure (EXAFS). It can be seen that the tilting and rotation of the MnO6 octahedra about the b-axis are responsible for the charge ordered CE-type antiferromagnetic ground state at low temperatures. In addition a shift in the position of the rare earth ion along the c-axis has to be considered to account for observed distribution of bond distances around the rare earth ion

SN 2021wvw: A core-collapse supernova at the sub-luminous, slower, and shorter end of Type IIPs

We present detailed multi-band photometric and spectroscopic observations and analysis of a rare core-collapse supernova SN 2021wvw, that includes photometric evolution up to 250 d and spectroscopic coverage up to 100 d post-explosion. A unique event that does not fit well within the general trends observed for Type II-P supernovae, SN 2021wvw shows an intermediate luminosity with a short plateau phase of just about 75 d, followed by a very sharp (~10 d) transition to the tail phase. Even in the velocity space, it lies at a lower velocity compared to a larger Type II sample. The observed peak absolute magnitude is -16.1 mag in r-band, and the nickel mass is well constrained to 0.020(6) Msol. Detailed hydrodynamical modeling using MESA+STELLA suggests a radially compact, low-metallicity, high-mass Red Supergiant progenitor (ZAMS mass=18 Msol), which exploded with ~0.2e51 erg/s leaving an ejecta mass of Mej~5 Msol. Significant late-time fallback during the shock propagation phase is also seen in progenitor+explosion models consistent with the light curve properties. As the faintest short-plateau supernova characterized to date, this event adds to the growing diversity of transitional events between the canonical ~100 d plateau Type IIP and stripped-envelope events.Accepted for publication in the Astrophysical Journal (18 pages, 13 figures, 4 tables

Far-Ultraviolet to Near-Infrared Observations of SN 2023ixf: A high energy explosion engulfed in complex circumstellar material

We present early-phase panchromatic photometric and spectroscopic coverage spanning far-ultraviolet (FUV) to the near-infrared (NIR) regime of the nearest hydrogen-rich core-collapse supernova in the last 25 years, SN~2023ixf. We observe early `flash' features in the optical spectra due to a confined dense circumstellar material (CSM). We observe high-ionization absorption lines Fe II, Mg II in the ultraviolet spectra from very early on. We also observe a multi-peaked emission profile of H-alpha in the spectrum beginning ~16 d, which indicates ongoing interaction of the SN ejecta with a pre-existing shell-shaped CSM having an inner radius of ~ 75 AU and an outer radius of ~140 AU. The shell-shaped CSM is likely a result of enhanced mass loss ~ 35 - 65 years before the explosion assuming a standard Red-Supergiant wind. Spectral modeling of the FUV, NUV, and the optical spectra during 9-12 d, using the radiative transfer spectrum synthesis code TARDIS indicates that the supernova ejecta could be well represented by a progenitor elemental composition greater than solar abundances. Based on early light curve models of Type II SNe, we infer that the nearby dense CSM confined to ~7+-3e14~cm(~45 AU) is a result of enhanced mass loss ~1e-(3.0+-0.5) Msol/yr two decades before the explosion.Comment: Submitted to AAS Journals, 4 figures, 2 table