Design of a 2-Bit Neural Network Quantizer for Laplacian Source

Achieving real-time inference is one of the major issues in contemporary neural network applications, as complex algorithms are frequently being deployed to mobile devices that have constrained storage and computing power. Moving from a full-precision neural network model to a lower representation by applying quantization techniques is a popular approach to facilitate this issue. Here, we analyze in detail and design a 2-bit uniform quantization model for Laplacian source due to its significance in terms of implementation simplicity, which further leads to a shorter processing time and faster inference. The results show that it is possible to achieve high classification accuracy (more than 96% in the case of MLP and more than 98% in the case of CNN) by implementing the proposed model, which is competitive to the performance of the other quantization solutions with almost optimal precision.     

Ergodic theory and visualization. I. Mesochronic plots for visualization of ergodic partition and invariant sets

We present a computational study of a visualization method for invariant sets based on ergodic partition theory, first proposed by Mezic? (Ph.D. thesis, Caltech, 1994) and Mezic? and Wiggins [Chaos 9, 213 (1999)]. The algorithms for computation of the time averages of observables on phase space are developed and used to provide an approximation of the ergodic partition of the phase space. We term the graphical representation of this approximation--based on time averages of observables--a mesochronic plot (from Greek: meso--mean, chronos--time). The method is useful for identifying low-dimensional projections (e.g., two-dimensional slices) of invariant structures in phase spaces of dimensionality bigger than two. We also introduce the concept of the ergodic quotient space, obtained by assigning a point to every ergodic set, and provide an embedding method whose graphical representation we call the mesochronic scatter plot. We use the Chirikov standard map as a well-known and dynamically rich example in order to illustrate the implementation of our methods. In addition, we expose applications to other higher dimensional maps such as the Froe?schle map for which we utilize our methods to analyze merging of resonances and, the three-dimensional extended standard map for which we study the conjecture on its ergodicity [I. Mezic?, Physica D 154, 51 (2001)]. We extend the study in our next paper [Z. Levnajic? and I. Mezic?, e-print arXiv:0808.2182] by investigating the visualization of periodic sets using harmonic time averages. Both of these methods are related to eigenspace structure of the Koopman operator [I. Mezic? and A. Banaszuk, Physica D 197, 101 (2004)].     

Chaotic dephasing in a double-slit scattering experiment

We design a computational experiment in which a quantum particle tunnels into a billiard of variable shape and scatters out of it through a double-slit opening on the billiard's base. The interference patterns produced by the scattered probability currents for a range of energies are investigated in relation to the billiard's geometry which is connected to its classical integrability. Four billiards with hierarchical integrability levels are considered: integrable, pseudointegrable, weak-mixing, and strongly chaotic. In agreement with the earlier result by Casati and Prosen [Phys. Rev. A 72, 032111 (2005)], we find the billiard's integrability to have a crucial influence on the properties of the interference patterns. In the integrable case, most experiment outcomes are found to be consistent with the constructive interference occurring in the usual double-slit experiment. In contrast to this, nonintegrable billiards typically display asymmetric interference patterns of smaller visibility characterized by weakly correlated wave function values at the two slits. Our findings indicate an intrinsic connection between the classical integrability and the quantum dephasing, which is responsible for the destruction of interference.     

Damping optimization of parameter dependent mechanical systems by rational interpolation

We consider an optimization problem related to semi-active damping of vibrating systems. The main problem is to determine the best damping matrix able to minimize influence of the input on the output of the system. We use a minimization criteria based on the \(\mathcal {H}_{2}\) system norm. The objective function is non-convex and the associated optimization problem typically requires a large number of objective function evaluations. We propose an optimization approach that calculates ‘interpolatory’ reduced order models, allowing for significant acceleration of the optimization process. In our approach, we use parametric model reduction (PMOR) based on the Iterative Rational Krylov Algorithm, which ensures good approximations relative to the \(\mathcal {H}_{2}\) system norm, aligning well with the underlying damping design objectives. For the parameter sampling that occurs within each PMOR cycle, we consider approaches with predetermined sampling and approaches using adaptive sampling, and each of these approaches may be combined with three possible strategies for internal reduction. In order to preserve important system properties, we maintain second-order structure, which through the use of modal coordinates, allows for very efficient implementation. The methodology proposed here provides a significant acceleration of the optimization process; the gain in efficiency is illustrated in numerical experiments.     

Elastomer-Clay Nanocomposites: Effect of Elastomer Polarity

Dynamic mechanical properties of non-polar and polar elastomer-based nanocomposites with Montmorillonite clay are studied in order to ascertain differences caused by elastomer's polarity. Natural as non-polar and polychloroprene as polar rubber are used to experimentally verify predictions based on different nature of elastomer-clay interactions in the two cases. The properties foretold and elucidated in terms of van der Waals interactions in the non-polar case and dipole-dipole interactions in the polar case agree well with experiment, concurrently sustaining general depiction of these unusual nanocomposites.     

Boundary between coherent and noncoherent small polaron motion: Influence of the phonon hardening

The transition from band to hopping conductivity of small polaron is examined within Holstein's molecular crystal model. The conditions under which each of these mechanisms prevail are formulated in terms of the values of the coupling constant S and adiabatic parameter B. Particular attention was paid to the possible influence of the polaron induced modification of phonon spectrum.     

Extraction of Peppermint Essential Oils and Lipophilic Compounds: Assessment of Process Kinetics and Environmental Impacts with Multiple Techniques

Consumers are becoming more mindful of their well-being. Increasing awareness of the many beneficial properties of peppermint essential oil (EO) has significantly increased product sales in recent years. Hydrodistillation (HD), a proven conventional method, and a possible alternative in the form of microwave-assisted hydrodistillation (MWHD) have been used to isolate peppermint EO. Standard Soxhlet and alternatively supercritical fluid (SFE), microwave-assisted, and ultrasound-assisted extraction separated the lipid extracts. The distillations employed various power settings, and the EO yield varied from 0.15 to 0.80%. The estimated environmental impact in terms of electricity consumption and CO₂ emissions suggested that MWHD is an energy efficient way to reduce CO₂ emissions. Different extraction methods and solvent properties affected the lipid extract yield, which ranged from 2.55 to 5.36%. According to the corresponding values of statistical parameters, empiric mathematical models were successfully applied to model the kinetics of MWHD and SFE processes.     

X‐ray Excited Optical Fluorescence and Diffraction Imaging of Reactivity and Crystallinity in a Zeolite Crystal: Crystallography and Molecular Spectroscopy in One

Structure–activity relationships in heterogeneous catalysis are challenging to be measured on a single‐particle level. For the first time, one X‐ray beam is used to determine the crystallographic structure and reactivity of a single zeolite crystal. The method generates μm‐resolved X‐ray diffraction (μ‐XRD) and X‐ray excited optical fluorescence (μ‐XEOF) maps of the crystallinity and Brønsted reactivity of a zeolite crystal previously reacted with a styrene probe molecule. The local gradients in chemical reactivity (derived from μ‐XEOF) were correlated with local crystallinity and framework Al content, determined by μ‐XRD. Two distinctly different types of fluorescent species formed selectively, depending on the local zeolite crystallinity. The results illustrate the potential of this approach to resolve the crystallographic structure of a porous material and its reactivity in one experiment via X‐ray induced fluorescence of organic molecules formed at the reactive centers.     

Self‐Complementary Dimers of Oxalamide‐Functionalized Resorcinarene Tetrabenzoxazines

Self‐complementarity is a useful concept in supramolecular chemistry, molecular biology and polymeric systems. Two resorcinarene tetrabenzoxazines decorated with four oxalamide groups were synthesized and characterized. The oxalamide groups possessed self‐complementary hydrogen bonding sites between the carbonyls and amide groups. The self‐complementary nature of the oxalamide groups resulted in self‐included dimeric assemblies. The hydrogen bonding interactions within the tetrabenzoxazines gave rise to the formation of dimers, which were confirmed by single‐crystal X‐ray diffractions analysis and supported by NMR spectroscopy and mass spectrometry. The self‐included dimers were connected by numerous and strong intermolecular N?H???O and C?H???O hydrogen bonds supplemented with C?H???π interactions, forming one‐dimensional polymers, which were then further linked into three‐dimensional networks.     

DNA binding and antitumor activities of platinum(IV) and zinc(II) complexes with some S-alkyl derivatives of thiosalicylic acid

A series of complexes of platinum(IV) (C1–C5) and zinc(II) (C6–C10) with S-alkyl derivatives of thiosalicylic acid were prepared and characterized. The interactions of the complexes with calf thymus DNA were analyzed by absorption (UV–Vis) and emission spectral studies (ethidium bromide displacement studies). The cytotoxic activities of complexes C1–C10 were determined against mouse B cell lymphocytic leukemia cells (BCL1), human B-prolymphocytic leukemia (JVM-13), mouse mammary carcinoma cells (4T1), and human mammary carcinoma cells (MDA-MB-468) and compared to the activities of the free ligand precursors and cisplatin. The cytotoxicities of the platinum(IV) and zinc(II) complexes toward mouse tumor cell lines were higher compared with their effects on human tumor cell lines. The zinc(II) complex C9 showed the highest antitumor activity toward the tested human cell lines, while the platinum(IV) complex C4 exhibited the highest antitumor activity toward mouse BCL1 and 4T1 cells. Both C4 and C9 have ligands derived from S-propyl thiosalicylic acid.