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We consider positive radial decreasing blow-up solutions of the semilinear heat equation \begin{equation*} u_t-\Delta u=f(u):=e^{u}L(e^{u}),\quad x\in \Omega,\ t>0, \end{equation*} where $\Omega=\mathbb{R}^n$ or $\Omega=B_R$ and $L$ is a slowly varying function (which includes for instance logarithms and their powers and iterates, as well as some strongly oscillating unbounded functions). We characterize the aymptotic blow-up behavior and obtain the sharp, global blow-up profile in the scale of the original variables $(x, t)$. Namely, assuming for instance $u_t\ge 0$, we have \begin{equation*} u(x,t)=G^{-1}\bigg(T-t+\frac{1}{8}\frac{|x|^2}{|\log |x||}\bigg)+o(1)\ \ \hbox{as $(x,t)\to (0,T)$,\quad where } G(X)=\int_{X}^{\infty} \frac{ds}{f(s)}ds. \end{equation*} This estimate in particular provides the sharp final space profile and the refined space-time profile. For exponentially growing nonlinearities, such results were up to now available only in the scale invariant case $f(u)=e^u$. Moreover, this displays a universal structure of the global blow-up profile, given by the resolvent $G^{-1}$ of the ODE composed with a fixed time-space building block, which is robust with respect to the factor $L(e^u)$., Comment: 24 pages

A system's internal dynamics and its interaction with the environment can be determined by tracking how external perturbations affect its transition rates between states. However, accurately measuring these rates poses a significant challenge, especially when they span a wide range of time scales. Here we introduce a broadband measurement method, called stochastic resonance spectroscopy (SRS), that operates in the frequency domain and quantifies the stochastic dynamics of atomic-scale quantum systems. We apply this method to determine spin switching rates in a scanning tunneling microscope over an extremely wide frequency range, from 199 ms^-1 for few-atom structures to 1.73 ns^-1 for individual atoms. SRS relies on the universal phenomenon of stochastic resonance which synchronizes stochastic dynamics to an oscillating perturbation. We develop an analytical theory that extracts quantitative transition rates from scanning tunneling microscopy measurements of the frequency-dependent tunnel current and show that the signal is dominated by homodyne detection. Our theory indicates that SRS is not limited to spin dynamics and we corroborate this by measuring transport dynamics through a bound state in a superconductor. We anticipate that the ability to characterize broadband stochastic dynamics at the atomic scale will enable insights into excited-state dynamics of quantum systems and even non-Markovian processes emerging from correlations with the environment., Comment: 12 pages, 5 figures

We characterize the asymptotic behavior near blowup points for positive solutions of the semilinear heat equation \begin{equation*} \partial_t u-\Delta u =f(u), \end{equation*} for nonlinearities which are genuinely non scale invariant, unlike in the standard case $f(u)=u^p$. Indeed, our results apply to a large class of nonlinearities of the form $f(u)=u^pL(u)$, where $p>1$ is Sobolev subcritical and $L$ is a slowly varying function at infinity (which includes for instance logarithms and their powers and iterates, as well as some strongly oscillating functions). More precisely, denoting by $\psi$ the unique positive solution of the corresponding ODE $y'(t)=f(y(t))$ which blows up at the same time $T$, we show that if $a\in\Omega$ is a blowup point of $u$, then \begin{equation*} \lim_{t\to T}\frac{u(a+y\sqrt{T-t},t)}{\psi(t)}= 1,\quad \text{uniformly for $y$ bounded.} \end{equation*} Additional blow-up properties are obtained, including the compactness of the blow-up set for the Cauchy problem with decaying initial data.

Generative AI models have recently blossomed, significantly impacting artistic and musical traditions. Research investigating how humans interact with and deem these models is therefore crucial. Through a listening and reflection study, we explore participants' perspectives on AI- vs human-generated progressive metal, in symbolic format, using rock music as a control group. AI-generated examples were produced by ProgGP, a Transformer-based model. We propose a mixed methods approach to assess the effects of generation type (human vs. AI), genre (progressive metal vs. rock), and curation process (random vs. cherry-picked). This combines quantitative feedback on genre congruence, preference, creativity, consistency, playability, humanness, and repeatability, and qualitative feedback to provide insights into listeners' experiences. A total of 32 progressive metal fans completed the study. Our findings validate the use of fine-tuning to achieve genre-specific specialization in AI music generation, as listeners could distinguish between AI-generated rock and progressive metal. Despite some AI-generated excerpts receiving similar ratings to human music, listeners exhibited a preference for human compositions. Thematic analysis identified key features for genre and AI vs. human distinctions. Finally, we consider the ethical implications of our work in promoting musical data diversity within MIR research by focusing on an under-explored genre., Comment: Reviewed pre-print accepted for publication at ISMIR 2024

We consider the semilinear heat equation $$u_t-\Delta u=f(u) $$ for a large class of non scale invariant nonlinearities of the form $f(u)=u^pL(u)$, where $p>1$ is Sobolev subcritical and $L$ is a slowly varying function (which includes for instance logarithms and their powers and iterates, as well as some strongly oscillating functions). For any positive radial decreasing blow-up solution, we obtain the sharp, global blow-up profile in the scale of the original variables $(x, t)$, which takes the form: $$u(x,t)=(1+o(1))\,G^{-1}\bigg(T-t+\frac{p-1}{8p}\frac{|x|^2}{|\log |x||}\bigg), \ \hbox{as $(x,t)\to (0,T)$, \quad where } G(X)=\int_{X}^{\infty}\frac{ ds}{f(s)}.$$ This estimate in particular provides the sharp final space profile and the refined space-time profile. As a remarkable fact and completely new observation, our results reveal a {\it structural universality} of the global blow-up profile, being given by the "resolvent" $G^{-1}$ of the ODE, composed with a universal, time-space building block, which is the same as in the pure power case., Comment: 30 pages; minor corrections with respect to v1

Fake news significantly influence our society. They impact consumers, voters, and many other societal groups. While Fake News exist for a centuries, Generative AI brings fake news on a new level. It is now possible to automate the creation of masses of high-quality individually targeted Fake News. On the other end, Generative AI can also help detecting Fake News. Both fields are young but developing fast. This survey provides a comprehensive examination of the research and practical use of Generative AI for Fake News detection and creation in 2024. Following the Structured Literature Survey approach, the paper synthesizes current results in the following topic clusters 1) enabling technologies, 2) creation of Fake News, 3) case study social media as most relevant distribution channel, 4) detection of Fake News, and 5) deepfakes as upcoming technology. The article also identifies current challenges and open issues., Comment: 16 pages, 2 figures. Submitted to ACM Transactions on Intelligent Systems and Technology (ACM TIST). Added references

A factorisation problem in the symmetric group is central if any two permutations in the same conjugacy class have the same number of factorisations. We give the first fully combinatorial proof of the centrality of transitive star factorisations that is valid in all genera, which answers a natural question of Goulden and Jackson from 2009. Our proof is through a bijection to a class of monotone double Hurwitz factorisations. These latter factorisations are also not obviously central, so we also give a combinatorial proof of their centrality. As a corollary we obtain new formulae for some monotone double Hurwitz numbers, and a new relation between Hurwitz and monotone Hurwitz numbers. We also generalise a theorem of Goulden and Jackson from 2009 that states that the transitive power of Jucys-Murphy elements are central. Our theorem states that the transitive image of any symmetric function evaluated at Jucys-Murphy elements is central, which gives a transitive version of Jucys' original result from 1974.

Designing terahertz sensors with high sensitivity to detect nanoscale thin films and single biomolecule presents a significant challenge, and addressing these obstacles is crucial for unlocking their full potential in scientific research and advanced applications. This work presents a strategy for the design optimization of metamaterial sensors employed in the detection of small amounts of dielectric materials. The sensors usually utilize the shift of the resonance frequency as an indicator of the presence of the analyte. The amount of shifting depends on intrinsic properties (electric field distribution, quality factor, and mode volume) of the bare cavity, as well as the overlap volume of its high-electric-field zone(s) and the analyte. Guided by the simplified dielectric perturbation theory, interdigitated electric split-ring resonators (ID-eSRR) are devised to significantly enhance the detection sensitivity for thin-film analytes compared to eSRRs without interdigitated fingers in the SRR gap region. The fingers of the ID-eSRR metamaterial sensor redistribute the electric field, creating strongly localized field enhancements that substantially boost the interaction with the analyte. Additionally, the periodic change of the orientation of the inherent anti-phase electric field in the interdigitated structure reduces radiation loss, leading to a higher Q-factor. Experiments with e-beam-fabricated ID-eSRR sensors operating at around 300 GHz demonstrate a remarkable frequency shift of 33.5 GHz upon deposition of a SiO2 layer with a thickness of 150 nm as an analyte simulant. The figure of merit (FOM) improves by over 50 times compared to structures without interdigitated fingers. This rational design option opens a promising avenue for highly sensitive detection of thin films and trace biomolecules., Comment: 16pages, 6 figures

We show that for the product of two fixed point free conjugacy classes, the average number of cycles is always very similar. Specifically, our main result is that for a randomly chosen pair of fixed point free permutations of cycle types $\alpha$ and $\beta$, the average number of cycles in their product is between $H_n-3$ and $H_n+1$, where $H_n$ is the harmonic number.

Recent work in the field of symbolic music generation has shown value in using a tokenization based on the GuitarPro format, a symbolic representation supporting guitar expressive attributes, as an input and output representation. We extend this work by fine-tuning a pre-trained Transformer model on ProgGP, a custom dataset of 173 progressive metal songs, for the purposes of creating compositions from that genre through a human-AI partnership. Our model is able to generate multiple guitar, bass guitar, drums, piano and orchestral parts. We examine the validity of the generated music using a mixed methods approach by combining quantitative analyses following a computational musicology paradigm and qualitative analyses following a practice-based research paradigm. Finally, we demonstrate the value of the model by using it as a tool to create a progressive metal song, fully produced and mixed by a human metal producer based on AI-generated music., Comment: Pre-print accepted for publication at CMMR2023

In this paper, we consider the moments of statistics on conjugacy classes of the colored permutation groups $\mathfrak{S}_{n,r}=\mathbb{Z}_r\wr \mathfrak{S}_n$. We first show that any fixed moment coincides on all conjugacy classes where all cycles have sufficiently long length. Additionally, for permutation statistics that can be realized via a process we call symmetric extensions, these moments are polynomials in $n$. Finally, for the descent statistic on the hyperoctahedral group $B_n\cong \mathfrak{S}_{n,2}$, we show that its distribution on conjugacy classes without short cycles satisfies a central limit theorem. Our results build on and generalize previous work of Fulman (\textit{J. Comb. Theory Ser. A.}, 1998), Hamaker and Rhoades (arXiv, 2022), and Campion Loth, Levet, Liu, Stucky, Sundaram, and Yin (arXiv, 2023). In particular, our techniques utilize the combinatorial framework introduced by Campion Loth, Levet, Liu, Stucky, Sundaram, and Yin.

Machine-learning methods rely on sufficiently large dataset to learn data distributions. They are widely used in research in X-Ray Computed Tomography, from low-dose scan denoising to optimisation of the reconstruction process. The lack of datasets prevents the scalability of these methods to realistic 3D problems. We develop a 3D procedural dataset in order to produce samples for data-driven algorithms. It is made of a meshed model of a left hand and a script to randomly change its anatomic properties and pose whilst conserving realistic features. This open-source solution relies on the freeware Blender and its Python core. Blender handles the modelling, the mesh and the generation of the hand's pose, whilst Python processes file format conversion from obj file to matrix and functions to scale and center the volume for further processing. Dataset availability and quality drives research in machine-learning. We design a dataset that weighs few megabytes, provides truthful samples and proposes continuous enhancements using version control. We anticipate this work to be a starting point for anatomically accurate procedural datasets. For instance, by adding more internal features and fine tuning their X-Ray attenuation properties.

We introduce the notion of a weighted inversion statistic on the symmetric group, and examine its distribution on each conjugacy class. Our work generalizes the study of several common permutation statistics, including the number of inversions, the number of descents, the major index, and the number of excedances. As a consequence, we obtain explicit formulas for the first moments of several statistics by conjugacy class. We also show that when the cycle lengths are sufficiently large, the higher moments of arbitrary permutation statistics are independent of the conjugacy class. Fulman (J. Comb. Theory Ser. A., 1998) previously established this result for major index and descents. We obtain these results, in part, by generalizing the techniques of Fulman (ibid.), and introducing the notion of permutation constraints. For permutation statistics that can be realized via symmetric constraints, we show that each moment is a polynomial in the degree of the symmetric group., Comment: We would also like to express our gratitude to Yan Zhuang for kindly alerting us to the arXiv paper of Hamaker and Rhoades (arXiv:2206.06567), after seeing the first version of the present paper. We also thank Zach Hamaker for taking the time to explain the results of the Hamaker--Rhoades paper and its overlap with the present work

We are interested in the distribution of the number of faces across all the $2-$cell embeddings of a graph, which is equivalent to the distribution of genus by Euler's formula. In order to study this distribution, we consider the local distribution of faces at a single vertex. We show an asymptotic uniformity on this local face distribution which holds for any graph with large vertex degrees. We use this to study the usual face distribution of the complete graph. We show that in this case, the local face distribution determines the face distribution for almost all of the whole graph. We use this result to show that a portion of the complete graph of size $(1-o(1))|K_n|$ has the same face distribution as the set of all permutations, up to parity. Along the way, we prove new character bounds and an asymptotic uniformity on conjugacy class products., Comment: To appear in European Journal of Combinatorics

A random 2-cell embedding of a connected graph $G$ in some orientable surface is obtained by choosing a random local rotation around each vertex. Under this setup, the number of faces or the genus of the corresponding 2-cell embedding becomes a random variable. Random embeddings of two particular graph classes, those of a bouquet of $n$ loops and those of $n$ parallel edges connecting two vertices, have been extensively studied and are well-understood. However, little is known about more general graphs. The results of this paper explain why Monte Carlo methods cannot work for approximating the minimum genus of graphs. In his breakthrough work [Permutation-partition pairs, JCTB 1991], Stahl developed the foundation of "random topological graph theory". Most of his results have been unsurpassed until today. In our work, we analyze the expected number of faces of random embeddings (equivalently, the average genus) of a graph $G$. It was very recently shown that for any graph $G$, the expected number of faces is at most linear. We show that the actual expected number of faces $F(G)$ is almost always much smaller. In particular, we prove: 1) $\frac{1}{2}\ln n - 2 < \mathbb{E}[F(K_n)] \le 3.65 \ln n +o(1)$. 2) For random graphs $G(n,p)$ ($p=p(n)$), we have $\mathbb{E}[F(G(n,p))] \le \ln^2 n+\frac{1}{p}$. 3) For random models $B(n,\Delta)$ containing only graphs, whose maximum degree is at most $\Delta$, we get stronger bounds $\mathbb{E}[F(B(n,\Delta))]=\Theta(\ln n)$., Comment: Accepted at the 35th ACM-SIAM Symposium on Discrete Algorithms (SODA 2024). 55 pages, 10 figures

A random 2-cell embedding of a given graph $G$ is obtained by choosing a random local rotation around every vertex. We analyze the expected number of faces of such an embedding, which is equivalent to studying its average genus. In 1991, Stahl proved that the expected number of faces in a random embedding of an arbitrary graph of order $n$ is at most $n\log(n)$. While there are many families of graphs whose expected number of faces is $\Theta(n)$, none are known where the expected number would be super-linear. This lead to the conjecture that there is a linear upper bound. In this note we confirm the conjecture by proving that for any $n$-vertex multigraph, the expected number of faces in a random 2-cell embedding is at most $n(1+H_m)$, where $m$ is the maximum edge-multiplicity and $H_m$ denotes the $m$th harmonic number. This bound is best possible up to a constant factor.

An increasing number of large-scale multi-modal research initiatives has been conducted in the typically developing population, as well as in psychiatric cohorts. Missing data is a common problem in such datasets due to the difficulty of assessing multiple measures on a large number of participants. The consequences of missing data accumulate when researchers aim to explore relationships between multiple measures. Here we aim to evaluate different imputation strategies to fill in missing values in clinical data from a large (total N=764) and deeply characterised (i.e. range of clinical and cognitive instruments administered) sample of N=453 autistic individuals and N=311 control individuals recruited as part of the EU-AIMS Longitudinal European Autism Project (LEAP) consortium. In particular we consider a total of 160 clinical measures divided in 15 overlapping subsets of participants. We use two simple but common univariate strategies, mean and median imputation, as well as a Round Robin regression approach involving four independent multivariate regression models including a linear model, Bayesian Ridge regression, as well as several non-linear models, Decision Trees, Extra Trees and K-Neighbours regression. We evaluate the models using the traditional mean square error towards removed available data, and consider in addition the KL divergence between the observed and the imputed distributions. We show that all of the multivariate approaches tested provide a substantial improvement compared to typical univariate approaches. Further, our analyses reveal that across all 15 data-subsets tested, an Extra Trees regression approach provided the best global results. This allows the selection of a unique model to impute missing data for the LEAP project and deliver a fixed set of imputed clinical data to be used by researchers working with the LEAP dataset in the future., Comment: 22 pages, 3 figures, 3 tables

A metal oxide support and a catalytically active metal are the two main ingredients for complex catalysts used in heterogeneous catalysis. The gas environment can change the catalyst during the reaction, modifying its structural and electronic properties. Here, we use monochromated electron energy loss spectroscopy (EELS) to reveal hydrogen-pressure-dependent changes of the electronic structure at the Pd/rutile-TiO$_2$ interface in an environmental transmission electron microscope (ETEM). Hydrogen-induced changes are observed in rutile-TiO$_2$ within $2$~nm from the interface at $10$~Pa of hydrogen pressure, in the Ti $L_{3,2}$ EEL spectra. Lower pressures such as $1$~Pa show no changes in the EEL spectra. We attribute the observed changes in the EEL spectra to hydrogen-induced defects accumulating in the vicinity of the interface. Based on DFT calculations, we developed a thermodynamic multistate defect (TMD) model of the interface and the bulk of the rutile-TiO$_2$. This TMD model predicts high concentrations of positively charged defects accumulating at the interface. The presence of the Schottky barrier stabilizes these defects by significantly lowering their formation energy. Our findings provide important new insights into catalytic processes taking place at metal/metal oxide interfaces in hydrogen gas environments., Comment: 18 pages, 12 figures

Random 2-cell embeddings of a given graph $G$ are obtained by choosing a random local rotation around every vertex. We analyze the expected number of faces, $\mathbb{E}[F_G]$, of such an embedding which is equivalent to studying its average genus. So far, tight results are known for two families called monopoles and dipoles. We extend the dipole result to a more general family called multistars, i.e., loopless multigraphs in which there is a vertex incident with all the edges. In particular, we show that the expected number of faces of every multistar with $n$ nonleaf edges lies in an interval of length $2/(n + 1)$ centered at the expected number of faces of an $n$-edge dipole. This allows us to derive bounds on $\mathbb{E}[F_G]$ for any given graph $G$ in terms of vertex degrees. We conjecture that $\mathbb{E}[F_G ] \le O(n)$ for any simple $n$-vertex graph $G$., Comment: 15 pages, 2 figures. Accepted to European conference on combinatorics, graph theory and applications (EUROCOMB) 2021

We present a practical approach for constructing meshes of general rough surfaces with given autocorrelation functions based on the unstructured meshes of nominally smooth surfaces. The approach builds on a well-known method to construct correlated random numbers from white noise using a decomposition of the autocorrelation matrix. We discuss important details arising in practical applications to the physicalmodeling of surface roughness and provide a software implementation to enable use of the approach with a broad range of numerical methods in various fields of science and engineering., Comment: 11 pages, 5 figures

We present the appearance of negative differential resistance (NDR) in spin-dependent electron transport through a few-atom spin-chain. A chain of three antiferromagnetically coupled Fe atoms(Fe trimer) was positioned on a Cu2N/Cu(100) surface and contacted with the spin-polarized tip of a scanning tunneling microscope, thus coupling the Fe trimer to one non-magnetic and one magnetic lead. Pronounced NDR appears at the low bias of 7 mV where inelastic electron tunneling dynamically locks the atomic spin in a long-lived excited state. This causes a rapid increase of the magnetoresistance between spin-polarized tip and Fe trimer and quenches elastic tunneling. By varying the coupling strength between tip and Fe trimer we find that in this transport regime the dynamic locking of the Fe trimer competes with magnetic exchange interaction, which statically forces the Fe trimer into the high-magnetoresistance state and removes the NDR.

The miniaturization of semiconductor devices to the scales where small numbers of dopants can control device properties requires the development of new techniques capable of characterizing their dynamics. Investigating single dopants requires sub-nanometer spatial resolution which motivates the use of scanning tunneling microscopy (STM), however, conventional STM is limited to millisecond temporal resolution. Several methods have been developed to overcome this shortcoming. Among them is all-electronic time-resolved STM, which is used in this work to study dopant dynamics in silicon with nanosecond resolution. The methods presented here are widely accessible and allow for local measurement of a wide variety of dynamics at the atomic scale. A novel time-resolved scanning tunneling spectroscopy technique is presented and used to efficiently search for dynamics.

Superconducting properties change in confined geometries. Here we study the effects of strong confinement in nanosized Pb-islands on Si(111) 7x7. Small hexagonal islands with diameters less than 50 nm and a uniform height of 7 atomic layers are formed by depositing Pb at low temperature and annealing at 300 K. We measure the tunneling spectra of individual Pb-nanoislands using a low-temperature scanning tunneling microscope operated at 0.6 K, and follow the narrowing of the superconducting gap as a function of magnetic field. We find the critical magnetic field, at which the superconducting gap vanishes, reaches several Tesla, which represents a greater than 50-fold enhancement compared to the bulk value. By independently measuring the size of the superconducting gap, and the critical magnetic field that quenches superconductivity for a range of nanoislands we can correlate these two fundamental parameters and estimate the maximal achievable critical field for 7 ML Pb-nanoislands to 7 T.

Heterogeneous atomic magnetic chains are built by atom manipulation on a Cu$_2$N/Cu (100) substrate. Their magnetic properties are studied and rationalized by a combined scanning tunneling microscopy (STM) and density functional theory (DFT) work completed by model Hamiltonian studies. The chains are built using Fe and Mn atoms ontop of the Cu atoms along the N rows of the Cu$_2$N surface. Here, we present results for FeMn$_x$ ($x$=1...6) chains emphasizing the evolution of the geometrical, electronic, and magnetic properties with chain size. By fitting our results to a Heisenberg Hamiltonian we have studied the exchange-coupling matrix elements $J$ for different chains. For the shorter chains, $x \leq 2$, we have included spin-orbit effects in the DFT calculations, extracting the magnetic anisotropy energy. Our results are also fitted to a simple anisotropic spin Hamiltonian and we have extracted values for the longitudinal-anisotropy $D$ and transversal-anisotropy $E$ constants. These parameters together with the values for $J$ allow us to compute the magnetic excitation energies of the system and to compare them with the experimental data., Comment: 10 pages 8 figures

The ability to sense the magnetic state of individual magnetic nano-objects is a key capability for powerful applications ranging from readout of ultra-dense magnetic memory to the measurement of spins in complex structures with nanometer precision. Magnetic nano-objects require extremely sensitive sensors and detection methods. Here we create an atomic spin sensor consisting of three Fe atoms and show that it can detect nanoscale antiferromagnets through minute surface-mediated magnetic interaction. Coupling, even to an object with no net spin and having vanishing dipolar stray field, modifies the transition matrix element between two spin states of the Fe-atom-based spin sensor that changes the sensor's spin relaxation time. The sensor can detect nanoscale antiferromagnets at up to three nanometers distance and achieves an energy resolution of 10 micro-electronvolts surpassing the thermal limit of conventional scanning probe spectroscopy. This scheme permits simultaneous sensing of multiple antiferromagnets with a single spin sensor integrated onto the surface., Comment: 30 pages main text, 6 figures, Supplementary materials not inculded

As the ultimate miniaturization of semiconductor devices approaches, it is imperative that the effects of single dopants be clarified. Beyond providing insight into functions and limitations of conventional devices, such information enables identification of new device concepts. Investigating single dopants requires sub-nanometre spatial resolution, making scanning tunnelling microscopy an ideal tool. However, dopant dynamics involve processes occurring at nanosecond timescales, posing a significant challenge to experiment. Here we use time-resolved scanning tunnelling microscopy and spectroscopy to probe and study transport through a dangling bond on silicon before the system relaxes or adjusts to accommodate an applied electric field. Atomically resolved, electronic pump-probe scanning tunnelling microscopy permits unprecedented, quantitative measurement of time-resolved single dopant ionization dynamics. Tunnelling through the surface dangling bond makes measurement of a signal that would otherwise be too weak to detect feasible. Distinct ionization and neutralization rates of a single dopant are measured and the physical process controlling those are identified.

We report on the magnetic properties of Fe and Co adatoms on a Cu$_{2}$N/Cu(100)-$c(2 \times 2)$ surface investigated by x-ray magnetic dichroism measurements and density functional theory (DFT) calculations including the local coulomb interaction. We compare these results with properties formerly deduced from STM spin excitation spectroscopy (SES) performed on the individual adatoms. In particular we focus on the values of the local magnetic moments determined by XMCD compared to the expectation values derived from the description of the SES data.The angular dependence of the projected magnetic moments along the magnetic field, as measured by XMCD, can be understood on the basis of the SES Hamiltonian. In agreement with DFT, the XMCD measurements show large orbital contributions to the total magnetic moment for both magnetic adatoms.

Ulm's Theorem presents invariants that classify countable abelian torsion groups up to isomorphism. Barwise and Eklof extended this result to the classification of arbitrary abelian torsion groups up to $L_{\infty \omega}$-equivalence. In this paper, we extend this classification to a class of mixed $\mathbb{Z}_p$-modules which includes all Warfield modules and is closed under $L_{\infty\omega}$-equivalence. The defining property of these modules is the existence of what we call a partial decomposition basis, a generalization of the concept of decomposition basis. We prove a complete classification theorem in $L_{\infty\omega}$ using invariants deduced from the classical Ulm and Warfield invariants.

Quantum entanglement permeates the complex ground states of correlated electron materials defying single-particle descriptions. Coupled magnetic atoms have potential as model systems for entanglement in condensed matter giving the opportunity to create artificial many-body states which can be controlled by tuning the underlying interactions. They provide an avenue to unravel the complexities of correlated-electron materials. Here we use low temperature scanning tunnelling microscopy (STM) and atomic manipulation to tune entanglement in chains of magnetic atoms. We find that a Kondo singlet state can emerge from this entanglement. The many electron Kondo state is based on the screening of the entangled spin ground state of the chain by substrate electrons and can be engineered to envelop at least ten magnetic atoms. The concomitant Kondo resonance measured in the differential conductance enables the electric read-out of entanglement. By tuning composition and coupling strength within atomic chains it is possible to create model spin chains with defined entanglement. This lays the foundation for a new class of experiments to construct exotic correlated-electron materials atom by atom., Comment: 15 pages, 4 figures, Supplementary Information

Spin-resolved scanning tunneling microscopy is employed to quantitatively determine the spin-polarization of the magnetic field-split Kondo state. Tunneling conductance spectra of a Kondo-screened magnetic atom are evaluated within a simple model taking into account inelastic tunneling due to spin excitations and two Kondo peaks positioned symmetrically around the Fermi energy. We fit the spin state of the Kondo-screened atom with a Spin Hamiltonian independent of the Kondo effect and account for Zeeman-splitting of the Kondo peak in the magnetic field. We find that the width and the height of the Kondo peaks scales with the Zeeman energy. Our observations are consistent with full spin-polarization of the Kondo peaks, i.e., a majority spin peak below the Fermi energy and a minority spin peak above.

A wide class of nanomagnets shows striking quantum behavior, known as quantum spin tunneling (QST): instead of two degenerate ground states with opposite magnetizations, a bonding-antibonding pair forms, resulting in a splitting of the ground state doublet with wave functions linear combination of two classically opposite magnetic states, leading to the quenching of their magnetic moment. Here we study how QST is destroyed and classical behavior emerges in the case of magnetic adatoms, as the strength of their coupling, either to the substrate or to each other, is increased. Both spin-substrate and spin-spin coupling renormalize the QST splitting to zero allowing the environmental decoherence to eliminate superpositions between classical states, leading to the emergence of spontaneous magnetization., Comment: 5 pages, 4 figures

Triethylsilylethynyl anthradithiophene (TESADT) holds considerable promise for organic transistor applications due to the high electrical mobilities attained by post-deposition crystallization using solvent vapour annealing. We have studied thermal annealing as an alternative route to post-deposition crystallization of TESADT films. Thermal annealing initially appears promising, producing mm-sized crystal domains, but poor electrical performance is obtained, which we attribute to a combination of crack formation and potentially also structural transition during the anneal process. We also find that illumination has a significant positive effect on crystallization, possibly due to an optically-induced enhancement in molecular mobility during annealing. This suggests further studies of how solvent exposure, heat, substrate surface properties and particularly light exposure influence the ordering kinetics of TESADT are warranted., Comment: In press for Journal of Organic Semiconductors

Electric double layer supercapacitors are a fast-rising class of high-power energy storage devices based on porous electrodes immersed in a concentrated electrolyte or ionic liquid. As of yet there is no microscopic theory to describe their surprisingly large capacitance per unit volume (volumetric capacitance) of ~ 100 F/cm^3, nor is there a good understanding of the fundamental limits on volumetric capacitance. In this paper we present a non-mean-field theory of the volumetric capacitance of a supercapacitor that captures the discrete nature of the ions and the exponential screening of their repulsive interaction by the electrode. We consider analytically and via Monte-Carlo simulations the case of an electrode made from a good metal and show that in this case the volumetric capacitance can reach the record values. We also study how the capacitance is reduced when the electrode is an imperfect metal characterized by some finite screening radius. Finally, we argue that a carbon electrode, despite its relatively large linear screening radius, can be approximated as a perfect metal because of its strong nonlinear screening. In this way the experimentally-measured capacitance values of ~ 100 F/cm^3 may be understood., Comment: 11 pages, 9 figures; extra discussion added; published version

We use Monte Carlo simulations to examine the simplest model of an ionic liquid, called the restricted primitive model, at a metal surface. We find that at moderately low temperatures the capacitance of the metal/ionic liquid interface is so large that the effective thickness of the electrostatic double-layer is up to 3 times smaller than the ion radius. To interpret these results we suggest an approach which is based on the interaction between discrete ions and their image charges in the metal surface and which therefore goes beyond the mean-field approximation. When a voltage is applied across the interface, the strong image attraction causes counterions to condense onto the metal surface to form compact ion-image dipoles. These dipoles repel each other to form a correlated liquid. When the surface density of these dipoles is low, the insertion of an additional dipole does not require much energy. This leads to a large capacitance $C$ that decreases monotonically with voltage $V$, producing a "bell-shaped" curve $C(V)$. We also consider what happens when the electrode is made from a semi-metal rather than a perfect metal. In this case, the finite screening radius of the electrode shifts the reflection plane for image charges to the interior of the electrode and we arrive at a "camel-shaped" $C(V)$. These predictions seem to be in qualitative agreement with experiment., Comment: 7 pages, 5 figures; some numerical comparisons added; schematic figure added, additional discussion of effect of electrode material, section added with comparison to semiconductor devices; plotting error fixed in Fig. 5

Mean-field theories claim that the capacitance of the double-layer formed at a metal/ionic conductor interface cannot be larger than that of the Helmholtz capacitor, whose width is equal to the radius of an ion. However, in some experiments the apparent width of the double-layer capacitor is substantially smaller. We propose an alternate, non-mean-field theory of the ionic double-layer to explain such large capacitance values. Our theory allows for the binding of discrete ions to their image charges in the metal, which results in the formation of interface dipoles. We focus primarily on the case where only small cations are mobile and other ions form an oppositely-charged background. In this case, at small temperature and zero applied voltage dipoles form a correlated liquid on both contacts. We show that at small voltages the capacitance of the double-layer is determined by the transfer of dipoles from one electrode to the other and is therefore limited only by the weak dipole-dipole repulsion between bound ions, so that the capacitance is very large. At large voltages the depletion of bound ions from one of the capacitor electrodes triggers a collapse of the capacitance to the much smaller mean-field value, as seen in experimental data. We test our analytical predictions with a Monte Carlo simulation and find good agreement. We further argue that our ``one-component plasma" model should work well for strongly asymmetric ion liquids. We believe that this work also suggests an improved theory of pseudo-capacitance., Comment: 19 pages, 14 figures; some Monte Carlo results and a section about aqueous solutions added

The capacitance of the double layer formed at a metal/ionic-conductor interface can be remarkably large, so that the apparent width of the double layer is as small as 0.3 \AA. Mean-field theories fail to explain such large capacitance. We propose an alternate theory of the ionic double layer which allows for the binding of discrete ions to their image charges in the metal. We show that at small voltages the capacitance of the double layer is limited only by the weak dipole-dipole repulsion between bound ions, and is therefore very large. At large voltages the depletion of bound ions from one of the capacitor electrodes triggers a collapse of the capacitance to the mean-field value., Comment: 4 pages, 3 figures; published version

Recent experiments measuring the electrical conductivity of DNA molecules highlight the need for a theoretical model of ion transport along a charged surface. Here we present a simple theory based on the idea of unbinding of ion pairs. The strong humidity dependence of conductivity is explained by the decrease in the electrostatic self-energy of a separated pair when a layer of water (with high dielectric constant) is adsorbed to the surface. We compare our prediction for conductivity to experiment, and discuss the limits of its applicability., Comment: 5 pages, 3 figures; one section and two illustrations added; figures updated and discussion added; typo fixed

Screening of a strongly charged macroion by its multivalent counterions can not be described in the framework of mean field Poisson-Boltzmann (PB) theory because multivalent counterions form a strongly correlated liquid (SCL) on the surface of the macroion. It was predicted that a distant counterion polarizes the SCL as if it were a metallic surface and creates an electrostatic image. The attractive potential energy of the image is the reason why the charge density of counterions decreases faster with distance from the charged surface than in PB theory. Using the Monte Carlo method to find the equilibrium distribution of counterions around the macroion, we confirm the existence of the image potential energy. It is also shown that due to the negative screening length of the SCL, $-2\xi$, the effective metallic surface is actually above the SCL by $|\xi|$., Comment: 9 pages, 6 figures; v5: new section added to address bulk screening by monovalent salt

In the Kondo effect, a localized magnetic moment is screened by forming a correlated electron system with the surrounding conduction electrons of a non-magnetic host. Spin S=1/2 Kondo systems have been investigated extensively in theory and experiments, but magnetic atoms often have a larger spin. Larger spins are subject to the influence of magnetocrystalline anisotropy, which describes the dependence of the magnetic moment's energy on the orientation of the spin relative to its surrounding atomic environment. Here we demonstrate the decisive role of magnetic anisotropy in the physics of Kondo screening. A scanning tunnelling microscope is used to simultaneously determine the magnitude of the spin, the magnetic anisotropy and the Kondo properties of individual magnetic atoms on a surface. We find that a Kondo resonance emerges for large-spin atoms only when the magnetic anisotropy creates degenerate ground-state levels that are connected by the spin flip of a screening electron. The magnetic anisotropy also determines how the Kondo resonance evolves in a magnetic field: the resonance peak splits at rates that are strongly direction dependent. These rates are well described by the energies of the underlying unscreened spin states., Comment: 14 pages, 4 figures, published in Nature Physics

Autocompensated Si-doped GaAs is studied with cross-sectional scanning tunneling spectroscopy (X-STS). The local electronic contrasts of substitutional Si(Ga) donors and Si(As) acceptors under the (110) cleavage plane are imaged with high resolution. Si(Ga) donor atoms exhibit radially symmetric contrasts. Si(As) acceptors have anisotropic features. The anisotropic acceptor contrasts are traced back to a tunnel process at the valence band edge. They reflect the probability density distribution of the localized acceptor hole state., Comment: 10 pages, 3 figures

The spatial distribution of the local density of states (LDOS) at Mn acceptors near the (110) surface of p-doped InAs is investigated by Scanning Tunneling Microscopy (STM). The shapes of the acceptor contrasts for different dopant depths under the surface are analyzed. Acceptors located within the first ten subsurface layers of the semiconductor show a lower symmetry than expected from theoretical predictions of the bulk acceptor wave function. They exhibit a (001) mirror asymmetry. The degree of asymmetry depends on the acceptor atoms' depths. The measured contrasts for acceptors buried below the 10th subsurface layer closely match the theoretically derived shape. Two effects are able to explain the symmetry reduction: the strain field of the surface relaxation and the tip-induced electric field., Comment: 8 pages, 4 figures

The electronic properties of shallow acceptors in p-doped GaAs{110} are investigated with scanning tunneling microscopy at low temperature. Shallow acceptors are known to exhibit distinct triangular contrasts in STM images for certain bias voltages. Spatially resolved I(V)-spectroscopy is performed to identify their energetic origin and behavior. A crucial parameter - the STM tip's work function - is determined experimentally. The voltage dependent potential configuration and band bending situation is derived. Ways to validate the calculations with the experiment are discussed. Differential conductivity maps reveal that the triangular contrasts are only observed with a depletion layer present under the STM tip. The tunnel process leading to the anisotropic contrasts calls for electrons to tunnel through vacuum gap and a finite region in the semiconductor., Comment: 11 pages, 8 figures

This paper addresses the issue of policy evaluation in Markov Decision Processes, using linear function approximation. It provides a unified view of algorithms such as TD(lambda), LSTD(lambda), iLSTD, residual-gradient TD. It is asserted that they all consist in minimizing a gradient function and differ by the form of this function and their means of minimizing it. Two new schemes are introduced in that framework: Full-gradient TD which uses a generalization of the principle introduced in iLSTD, and EGD TD, which reduces the gradient by successive equi-gradient descents. These three algorithms form a new intermediate family with the interesting property of making much better use of the samples than TD while keeping a gradient descent scheme, which is useful for complexity issues and optimistic policy iteration.

CEA, ANDRA and EDF are jointly developing the software platform ALLIANCES which aim is to produce a tool for the simulation of nuclear waste storage and disposal repository. This type of simulations deals with highly coupled thermo-hydro-mechanical and chemical (T-H-M-C) processes. A key objective of Alliances is to give the capability for coupling algorithms development between existing codes. The aim of this paper is to present coupling methodology use in the context of this software platform., Comment: 7 pages

Photo-induced synthesis and control over the size and shape of colloidal silver nanoparticles is investigated in contrast to photo-stimulated aggregation of small nanoparticles into large fractal-type structures. The feasibility of light-driven nanoengineering which enables manipulation of the sizes and shapes of the isolated nanoparticles is studied by varying the amount and type of the stabilizing agent and the type of optical irradiation., Comment: 10 pages, 7 figures, 11 images

A Laser-stimulated synthesis of large silver nanoaggregates consisting of hundreds to thousands of nanoparticles is investigated. It is shown that the morphology of the synthesized nanostructures can be controlled with light and monitored via the evolution of the colloid absorption spectra. A solution method is demonstrated that enables production of a bulk amount of metal nanoaggregates, which are of paramount importance for subwavelength concentration and dramatic enhancement of the electromagnetically-induced processes at the nanoscale., Comment: 10 pages, 8 figures, 13 references

In this paper, we study the group Pext(C,A) for locally compact abelian (LCA) groups A and C. Sufficient conditions are established for Pext(C,A) to coincide with the first Ulm subgroup of Ext(C,A). Some structural information on pure injectives in the category of LCA groups is obtained. Letting K denote the class of LCA groups which can be written as the topological direct sum of a compactly generated group and a discrete group, we determine the groups G in K which are pure injective in the category of LCA groups. Finally we describe those groups G in K such that every pure extension of G by a group in K splits and obtain a corresponding dual result., Comment: To appear in Rendiconti del Seminario Matematico della Universita di Padova

The possibilities for control over the size and properties of silver nanoaggregates with incoherent and laser light are investigated. The applications in nanoengineering and for giant enhancement of optical processes at nanoscale are discussed., Comment: 3 pages, 3 figures

This report presents the key results from the first two years of a program to develop experimental icing simulation capabilities for full-scale swept wings. This investigation was undertaken as a part of a larger collaborative research effort on ice accretion and aerodynamics for large-scale swept wings. Ice accretion and the resulting aerodynamic effect on large-scale swept wings presents a significant airplane design and certification challenge to air frame manufacturers, certification authorities, and research organizations alike. While the effect of ice accretion on straight wings has been studied in detail for many years, the available data on swept-wing icing are much more limited, especially for larger scales.