Miracle-dz/UniFAR-FTUs huggingface dataset:
Effect of Hydration on the Volume and Compressibility of Protein Molecules

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The Structure and Properties of Supercritical Water

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How to Query an Oracle? Efficient Strategies to Label Data

We consider the basic problem of querying an expert oracle for labeling a dataset in machine learning. This is typically an expensive and time consuming process and therefore, we seek ways to do so efficiently. The conventional approach involves comparing each sample with (the representative of) each class to find a match. In a setting with <inline-formula><tex-math notation="LaTeX">$N$</tex-math><alternatives><mml:math><mml:mi>N</mml:mi></mml:math><inline-graphic xlink:href="lahouti-ieq1-3118644.gif"/></alternatives></inline-formula> equally likely classes, this involves <inline-formula><tex-math notation="LaTeX">$N/2$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>N</mml:mi><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href="lahouti-ieq2-3118644.gif"/></alternatives></inline-formula> pairwise comparisons (queries per sample) on average. We consider a <inline-formula><tex-math notation="LaTeX">$k$</tex-math><alternatives><mml:math><mml:mi>k</mml:mi></mml:math><inline-graphic xlink:href="lahouti-ieq3-3118644.gif"/></alternatives></inline-formula>-ary query scheme with <inline-formula><tex-math notation="LaTeX">$k\geq 2$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>k</mml:mi><mml:mo>≥</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href="lahouti-ieq4-3118644.gif"/></alternatives></inline-formula> samples in a query that identifies (dis)similar items in the set while effectively exploiting the associated transitive relations. We present a randomized batch algorithm that operates on a round-by-round basis to label the samples and achieves a query rate of <inline-formula><tex-math notation="LaTeX">$O(\frac{N}{k^2})$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mfrac><mml:mi>N</mml:mi><mml:msup><mml:mi>k</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mfrac><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="lahouti-ieq5-3118644.gif"/></alternatives></inline-formula>. In addition, we present an adaptive greedy query scheme, which achieves an average rate of <inline-formula><tex-math notation="LaTeX">$\approx 0.2N$</tex-math><alternatives><mml:math><mml:mrow><mml:mo>≈</mml:mo><mml:mn>0</mml:mn><mml:mo>. </mml:mo><mml:mn>2</mml:mn><mml:mi>N</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href="lahouti-ieq6-3118644.gif"/></alternatives></inline-formula> queries per sample with triplet queries. For the proposed algorithms, we investigate the query rate performance analytically and with simulations. Empirical studies suggest that each triplet query takes an expert at most 50% more time compared with a pairwise query, indicating the effectiveness of the proposed <inline-formula><tex-math notation="LaTeX">$k$</tex-math><alternatives><mml:math><mml:mi>k</mml:mi></mml:math><inline-graphic xlink:href="lahouti-ieq7-3118644.gif"/></alternatives></inline-formula>-ary query schemes. We generalize the analyses to nonuniform class distributions when possible.
Reciprocal Relations in Irreversible Processes. II.

A general reciprocal relation, applicable to transport processes such as the conduction of heat and electricity, and diffusion, is derived from the assumption of microscopic reversibility. In the derivation, certain average products of fluctuations are considered. As a consequence of the general relation $S=k logW$ between entropy and probability, different (coupled) irreversible processes must be compared in terms of entropy changes. If the displacement from thermodynamic equilibrium is described by a set of variables ${\ensuremath{\alpha}}_{1},\ensuremath{\cdots},{\ensuremath{\alpha}}_{n}$, and the relations between the rates ${\stackrel{\ifmmode \dot{}\else \. {}\fi{}}{\ensuremath{\alpha}}}_{1},\ensuremath{\cdots},{\stackrel{\ifmmode \dot{}\else \. {}\fi{}}{\ensuremath{\alpha}}}_{n}$ and the "forces" $\frac{\ensuremath{\partial}S}{d{\ensuremath{\alpha}}_{1}},\ensuremath{\cdots},\frac{\ensuremath{\partial}S}{d{\ensuremath{\alpha}}_{n}}$ are linear, there exists a quadratic dissipation-function, $2\ensuremath{\Phi}(\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\alpha}},\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\alpha}})\ensuremath{\equiv}\ensuremath{\Sigma}{\ensuremath{\rho}}_{j}{\stackrel{\ifmmode \dot{}\else \. {}\fi{}}{\ensuremath{\alpha}}}_{\mathrm{ij}}{\stackrel{\ifmmode \dot{}\else \. {}\fi{}}{\ensuremath{\alpha}}}_{i}=\frac{\mathrm{dS}}{\mathrm{dt}}=\stackrel{\ifmmode \dot{}\else \. {}\fi{}}{S}(\ensuremath{\alpha},\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\alpha}})\ensuremath{\equiv}\ensuremath{\Sigma}(\frac{\ensuremath{\partial}S}{d{\ensuremath{\alpha}}_{j}}){\stackrel{\ifmmode \dot{}\else \. {}\fi{}}{\ensuremath{\alpha}}}_{j}$ (denoting definition by $\ensuremath{\equiv}$). The symmetry conditions demanded by microscopic reversibility are equivalent to the variation-principle $\stackrel{\ifmmode \dot{}\else \. {}\fi{}}{S}(\ensuremath{\alpha},\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\alpha}})\ensuremath{-}\ensuremath{\Phi}(\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\alpha}},\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\alpha}})=\mathrm{maximum},$ which determines ${\stackrel{\ifmmode \dot{}\else \. {}\fi{}}{\ensuremath{\alpha}}}_{1},\ensuremath{\cdots},{\stackrel{\ifmmode \dot{}\else \. {}\fi{}}{\ensuremath{\alpha}}}_{n}$ for prescribed ${\ensuremath{\alpha}}_{1},\ensuremath{\cdots},{\ensuremath{\alpha}}_{n}$. The dissipation-function has a statistical significance similar to that of the entropy. External magnetic fields, and also Coriolis forces, destroy the symmetry in past and future; reciprocal relations involving reversal of the field are formulated.
A Deep Convolutional Autoencoder for Automatic Motion Artifact Removal in Electrodermal Activity

<italic>Objective:</italic> This study aimed to develop a robust and data driven automatic motion artifacts (MA) removal technique from electrodermal activity (EDA) signal. <italic>Methods:</italic> we proposed a deep convolutional autoencoder (DCAE) approach for automatic MA removal in EDA signals. Our model was trained using several publicly available datasets that were collected using a wide variety of stimuli to cause EDA reactions; the sample size was large (<inline-formula><tex-math notation="LaTeX">$\mathbf{N}\ = \ 385\ \text{subjects}$</tex-math></inline-formula>). We trained and validated our DCAE network using both Gaussian white noise (GWN) and realistic MA data records collected using a novel circuitry in our lab. We further evaluated and compared the performance of our DCAE model with the existing methods on two independent and unseen datasets called Chon lab motion artifact dataset II (CMAD II) and central nervous system oxygen toxicity dataset (CNS-OT). <italic>Results:</italic> Our DCAE model showed significantly higher signal-to-noise-power-ratio improvement (<inline-formula><tex-math notation="LaTeX">$\mathbf{SN}{\mathbf{R}_{\mathbf{imp}}}$</tex-math></inline-formula>) and lower mean squared error (<inline-formula><tex-math notation="LaTeX">$\mathbf{MSE}$</tex-math></inline-formula>) when compared with that of the three previous methods (averaged <inline-formula><tex-math notation="LaTeX">$\boldsymbol{S\! N\! R}_\text{imp} = 35.25\,{\text{dB}}$</tex-math></inline-formula>, and <inline-formula><tex-math notation="LaTeX">${\boldsymbol{M\! S\! E\ }} = 0.028$</tex-math></inline-formula> on the MA-corrupted data). Moreover, the reconstructed EDAs from the CMAD II dataset had a mean correlation value of 0.78 (statistically significantly higher when compared with other methods) with the reference clean data from the motionless hand, whereas the raw MA-corrupted data had a correlation value of only 0.68. <italic>Conclusion:</italic> The results presented in the paper indicates that our DCAE can remove MAs with higher intensity where the existing methods fails. <italic>Significance:</italic> Proposed DCAE model can be used to recover a significant amount of otherwise discarded EDA data.
A new proof of Hamburger's Index Theorem on umbilical points

The Index Theorem of H. Hamburger states that the index J of an isolated umbilical point P on a real analytic surface in ffi,3 is not greater than 1. This confirms a conjecture of C. Caratheodory for the analytical case : "There exist at least two umbilical points on every ovaloid which is sufficiently smooth". G. Bol tried to give a simpler proof for this theorem. T. Klotz realized that there is a gap in Bol's proof so that the general case is not covered. She provided additional arguments for a complete proof but it turned out that she did not succeed completely. We use the same geometrical methods of blowing up certain singularities to solve this problem and succeed in giving a complete proof. The main steps are the following : The statement J(P) < 1 is equivalent to W(B) > 0 , where W is the winding number of a family of plane curves B(g, ti) = x(g, i? ) + iy(g, t? ) (p > 0, curve parameter •d mod 2ir) around the origin. We consider the Puiseux series of the zeros of x and y. They are of the form i? (p) = oo $o + r« £ tA',X with p = rP . A=0 For every step where we determine t^, this process provides us with a more and more refined approximation to parts of the base curve B (g fixed). The approximating curves may pass through the origin. This means that x and y have at least one common zero f of the form i? 0 + r» £ txrx + o^) . A=o In this case we apply a "modification rule" to the approximating curves. We give a lower bound for the intersection number of these modified curves with a line through the origin. Some of the zero crossings (called "singular cases") have to be investigated in more detail, i.e. we continue the blowing up process using the next coefficient of the corresponding Puiseux series. After a finite number of steps, there are no singular cases left and the process stops. By summing up the intersection numbers of all modified approximating curves we show that W(B) > 0 . Two points are crucial to the success of the new proof : We first formulate a new modification rule for higher order approximating curves. Second, controlling some constants related to these curves, we are able to give a lower bound of -2 for their intersection numbers. This finally results in a complete proof of Hamburger's Index Theorem.
Investigating the Effectiveness of Using GeoGebra in Associate Degree Mathematics Instruction

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