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In the realm of reinforcement learning (RL), accounting for risk is crucial for making decisions under uncertainty, particularly in applications where safety and reliability are paramount. In this paper, we introduce a general framework on Risk-Sensitive Distributional Reinforcement Learning (RS-DisRL), with static Lipschitz Risk Measures (LRM) and general function approximation. Our framework covers a broad class of risk-sensitive RL, and facilitates analysis of the impact of estimation functions on the effectiveness of RSRL strategies and evaluation of their sample complexity. We design two innovative meta-algorithms: \texttt{RS-DisRL-M}, a model-based strategy for model-based function approximation, and \texttt{RS-DisRL-V}, a model-free approach for general value function approximation. With our novel estimation techniques via Least Squares Regression (LSR) and Maximum Likelihood Estimation (MLE) in distributional RL with augmented Markov Decision Process (MDP), we derive the first $\widetilde{\mathcal{O}}(\sqrt{K})$ dependency of the regret upper bound for RSRL with static LRM, marking a pioneering contribution towards statistically efficient algorithms in this domain.

This work pioneers regret analysis of risk-sensitive reinforcement learning in partially observable environments with hindsight observation, addressing a gap in theoretical exploration. We introduce a novel formulation that integrates hindsight observations into a Partially Observable Markov Decision Process (POMDP) framework, where the goal is to optimize accumulated reward under the entropic risk measure. We develop the first provably efficient RL algorithm tailored for this setting. We also prove by rigorous analysis that our algorithm achieves polynomial regret $\tilde{O}\left(\frac{e^{|{\gamma}|H}-1}{|{\gamma}|H}H^2\sqrt{KHS^2OA}\right)$, which outperforms or matches existing upper bounds when the model degenerates to risk-neutral or fully observable settings. We adopt the method of change-of-measure and develop a novel analytical tool of beta vectors to streamline mathematical derivations. These techniques are of particular interest to the theoretical study of reinforcement learning., Comment: 38 pages

In recent years, advanced deep neural networks have required a large number of parameters for training. Therefore, finding a method to reduce the number of parameters has become crucial for achieving efficient training. This work proposes a training scheme for classical neural networks (NNs) that utilizes the exponentially large Hilbert space of a quantum system. By mapping a classical NN with $M$ parameters to a quantum neural network (QNN) with $O(\text{polylog} (M))$ rotational gate angles, we can significantly reduce the number of parameters. These gate angles can be updated to train the classical NN. Unlike existing quantum machine learning (QML) methods, the results obtained from quantum computers using our approach can be directly used on classical computers. Numerical results on the MNIST and Iris datasets are presented to demonstrate the effectiveness of our approach. Additionally, we investigate the effects of deeper QNNs and the number of measurement shots for the QNN, followed by the theoretical perspective of the proposed method. This work opens a new branch of QML and offers a practical tool that can greatly enhance the influence of QML, as the trained QML results can benefit classical computing in our daily lives., Comment: 7 pages, 3 figures

Quantum error correction (QEC) provides a practical path to fault-tolerant quantum computing through scaling to large qubit numbers, assuming that physical errors are sufficiently uncorrelated in time and space. In superconducting qubit arrays, high-energy impact events produce correlated errors, violating this key assumption. Following such an event, phonons with energy above the superconducting gap propagate throughout the device substrate, which in turn generate a temporary surge in quasiparticle (QP) density throughout the array. When these QPs tunnel across the qubits' Josephson junctions, they induce correlated errors. Engineering different superconducting gaps across the qubit's Josephson junctions provides a method to resist this form of QP tunneling. By fabricating all-aluminum transmon qubits with both strong and weak gap engineering on the same substrate, we observe starkly different responses during high-energy impact events. Strongly gap engineered qubits do not show any degradation in T1 during impact events, while weakly gap engineered qubits show events of correlated degradation in T1. We also show that strongly gap engineered qubits are robust to QP poisoning from increasing optical illumination intensity, whereas weakly gap engineered qubits display rapid degradation in coherence. Based on these results, gap engineering removes the threat of high-energy impacts to QEC in superconducting qubit arrays.

The fermionic Hubbard model (FHM)[1], despite its simple form, captures essential features of strongly correlated electron physics. Ultracold fermions in optical lattices[2, 3] provide a clean and well-controlled platform for simulating FHM. Doping its antiferromagnetic ground state at half filling, various exotic phases are expected to arise in the FHM simulator, including stripe order[4], pseudogap[5], and d-wave superconductors[6], offering valuable insights into high-temperature superconductivity[7{9]. Although notable progress, such as the observation of antiferromagnetic correlations over short[10] and extended distances[11], has been obtained, the antiferromagnetic phase has yet to be realized due to the significant challenges of achieving low temperatures in a large and uniform quantum simulator. Here, we report the observation of the antiferromagnetic phase transition in a three-dimensional fermionic Hubbard system comprising lithium-6 atoms in a uniform optical lattice with approximately 800,000 sites. When the interaction strength, temperature, and doping concentration are finely tuned to approach their respective critical values, sharp increases in the spin structure factor (SSF) are observed. These observations can be well described by a power-law divergence, with a critical exponent of 1.396 from the Heisenberg universality class[12]. At half filling and with optimal interaction strength, the measured SSF reaches 123(8), signifying the establishment of an antiferromagnetic phase. Our results set the stage for exploring the low-temperature phase diagram of FHM.

Fairness has become increasingly pivotal in machine learning for high-risk applications such as machine learning in healthcare and facial recognition. However, we see the deficiency in the previous logits space constraint methods. Therefore, we propose a novel framework, Logits-MMD, that achieves the fairness condition by imposing constraints on output logits with Maximum Mean Discrepancy. Moreover, quantitative analysis and experimental results show that our framework has a better property that outperforms previous methods and achieves state-of-the-art on two facial recognition datasets and one animal dataset. Finally, we show experimental results and demonstrate that our debias approach achieves the fairness condition effectively.

In the paper, we consider the extended Gross-Witten-Wadia unitary matrix model by introducing a logarithmic term in the potential. The partition function of the model can be expressed equivalently in terms of the Toeplitz determinant with the $(i,j)$-entry being the modified Bessel functions of order $i-j-\nu$, $\nu\in\mathbb{C}$. When the degree $n$ is finite, we show that the Toeplitz determinant is described by the isomonodromy $\tau$-function of the Painlev\'{e} III equation. As a double scaling limit, %In the double scaling limit as the degree $n\to\infty$, we establish an asymptotic approximation of the logarithmic derivative of the Toeplitz determinant, expressed in terms of the Hastings-McLeod solution of the inhomogeneous Painlev\'{e} II equation with parameter $\nu+\frac{1}{2}$. The asymptotics of the leading coefficient and recurrence coefficient of the associated orthogonal polynomials are also derived. We obtain the results by applying the Deift-Zhou nonlinear steepest descent method to the Riemann-Hilbert problem for orthogonal polynomials on the Hankel loop. The main concern here is the construction of a local parametrix at the critical point $z=-1$, where the $\psi$-function of the Jimbo-Miwa Lax pair for the inhomogeneous Painlev\'{e} II equation is involved., Comment: 41 pages, 14 figures

Large language models require updates to remain up-to-date or adapt to new domains by fine-tuning them with new documents. One key is memorizing the latest information in a way that the memorized information is extractable with a query prompt. However, LLMs suffer from a phenomenon called perplexity curse; despite minimizing document perplexity during fine-tuning, LLMs struggle to extract information through a prompt sentence. In this new knowledge acquisition and extraction, we find a very intriguing fact that LLMs can accurately answer questions about the first sentence, but they struggle to extract information described in the middle or end of the documents used for fine-tuning. Our study suggests that the auto-regressive training causes this issue; each token is prompted by reliance on all previous tokens, which hinders the model from recalling information from training documents by question prompts. To conduct the in-depth study, we publish both synthetic and real datasets, enabling the evaluation of the QA performance w.r.t. the position of the corresponding answer in a document. Our investigation shows that even a large model suffers from the perplexity curse, but regularization such as denoising auto-regressive loss can enhance the information extraction from diverse positions. These findings will be (i) a key to improving knowledge extraction from LLMs and (ii) new elements to discuss the trade-off between RAG and fine-tuning in adapting LLMs to a new domain.

Adaptive experimental design (AED) methods are increasingly being used in industry as a tool to boost testing throughput or reduce experimentation cost relative to traditional A/B/N testing methods. However, the behavior and guarantees of such methods are not well-understood beyond idealized stationary settings. This paper shares lessons learned regarding the challenges of naively using AED systems in industrial settings where non-stationarity is prevalent, while also providing perspectives on the proper objectives and system specifications in such settings. We developed an AED framework for counterfactual inference based on these experiences, and tested it in a commercial environment.

High-quality Extragalactic Legacy-field Monitoring (HELM) is a long-term observing program that photometrically monitors several well-studied extragalactic legacy fields with the Dark Energy Camera (DECam) imager on the CTIO 4m Blanco telescope. Since Feb 2019, HELM has been monitoring regions within COSMOS, XMM-LSS, CDF-S, S-CVZ, ELAIS-S1, and SDSS Stripe 82 with few-day cadences in the $(u)gri(z)$ bands, over a collective sky area of $\sim 38$ deg${\rm ^2}$. The main science goal of HELM is to provide high-quality optical light curves for a large sample of active galactic nuclei (AGNs), and to build decades-long time baselines when combining past and future optical light curves in these legacy fields. These optical images and light curves will facilitate the measurements of AGN reverberation mapping lags, as well as studies of AGN variability and its dependences on accretion properties. In addition, the time-resolved and coadded DECam photometry will enable a broad range of science applications from galaxy evolution to time-domain science. We describe the design and implementation of the program and present the first data release that includes source catalogs and the first $\sim 3.5$ years of light curves during 2019A--2022A., Comment: 11 pages, 8 figures, 4 tables, submitted to ApJS. Median source catalogs and light curves of individual objects are publicly available at https://ariel.astro.illinois.edu/helm/

We report scanning tunnelling microscopy (STM) and x-ray photoemission spectroscopy (XPS) measurements on uncapped and SrTiO3 (STO) capped NdNiO2 realized by pulsed-laser deposition and topotactic reduction process. We find that untreated NdNiO2 surfaces are insulating and contain Ni mostly in a nominal Ni2+ oxidation state. Room temperature STM shows signatures of a striped-like topographic pattern, possibly compatible with recent reports of ordered oxygen vacancies in uncapped nickelates due to incomplete oxygen de-intercalation of the upper layers. A metallic surface and a full Ni1+ oxidation state is recovered by ultra high vacuum annealing at 250 C, as shown by STM and XPS. STO-capped NdNiO2 films, on the other hand, show Ni mostly in Ni1+ configuration, but Nd 3d5/2 core level spectra have a relevant contribution from ligand 4f 4L states, suggesting the formation of a NdTiNiOx layer at the interface with the STO. By in situ unit-cell by unit-cell Ar-ion sputtering removal of the STO capping and of the non stoichiometric interface layer, we were able to address the surface electronic properties of these samples, as shown by high resolution valence band photoemission spectroscopy. The results provide insights in the properties of infinite-layer NdNiO2 thin films prepared by the CaH2 topotactic reduction of perovskite NdNiO3 and suggest methods to improve their surface quality.

Polarimetric infrared detection bolsters IR thermography by leveraging the polarization of light. Optical anisotropy, i.e., birefringence and dichroism, can be leveraged to achieve polarimetric detection. Recently, giant optical anisotropy was discovered in quasi-1D narrow-bandgap hexagonal perovskite sulfides, A1+xTiS3, specifically BaTiS3[1,2] and Sr9/8TiS3[3,4]. In these materials, the critical role of atomic-scale structure modulations[4,5] in the unconventional electrical[5,6], optical[7,8], and thermal[7,9] properties raises the broader question of other materials that belong to this family. To address this issue, for the first time, we synthesized high-quality single crystals of a largely unexplored member of the A1+xTiX3 (X = S, Se) family, BaTiSe3. Single-crystal X-ray diffraction determined the room-temperature structure with the P31c space group, which is a superstructure of the earlier reported[10] P63/mmc structure. The crystal structure of BaTiSe3 features antiparallel c-axis displacements similar to BaTiS3,[2] but is of lower symmetry. Polarization-resolved Raman and Fourier transform infrared (FTIR) spectroscopy were used to characterize the optical anisotropy of BaTiSe3, whose refractive index along the ordinary (perpendicular to c) and extraordinary (parallel to c) optical axes was quantitatively determined by combining ellipsometry studies with FTIR. With a giant birefringence {\Delta}n~0.9, BaTiSe3 emerges as a new candidate for miniaturized birefringent optics for mid-wave infrared to long-wave infrared imaging.

Rydberg-assisted atomic electrometry with thermal vapors offers a promising approach for detecting external electric fields. This technique, however, has proven quite challenging for measuring low frequencies because of the effects of metal-alkali atoms absorbing on the interior surface of the vacuum enclosure. We apply high-contrast Rydberg-electromagnetically-induced-transparency (EIT) spectroscopy to investigate the impact systematically, including laser power and electric field. Our system enhances frequency measurements below 10 Hz, demonstrating significant progress in improving the performance of Rydberg atomic electrometry. Consequently, our study reveals a standard quantum limit for data capacity and experimentally illustrates it across bandwidths ranging from 10 Hz to 1 MHz. This study provides valuable insights for future precision measurements and field sensing applications., Comment: 7 pages, 5 figures

To represent the two-dimensional $N$-body delta-Bose gas for any integer $N\geq 2$, we construct an It\^{o} diffusion satisfying the strong Markov property and establish an associated Feynman-Kac-type formula. Among several properties, the diffusion is singular to the Brownian motion for showing almost sure contacts of particles and has a supercritical drift coefficient in the sense of a Ladyzhenskaya-Prodi-Serrin-type condition. Despite the supercriticality, the construction of the diffusion process and the relevant distributional properties for the Feynman-Kac-type formula are obtained by locally transforming the relative motions in two-body interactions and the necessary free motions. The central mechanism making this reduction to two-body interaction possible is the "no triple contacts" of particles, observed earlier in the functional integrals of the two-dimensional delta-Bose gas and now extended to the stochastic process level., Comment: 122 pages

By formulating the floorplanning of VLSI as a mixed-variable optimization problem, this paper proposes to solve it by memetic algorithms, where the discrete orientation variables are addressed by the distribution evolutionary algorithm based on a population of probability model (DEA-PPM), and the continuous coordination variables are optimized by the conjugate sub-gradient algorithm (CSA). Accordingly, the fixed-outline floorplanning algorithm based on CSA and DEA-PPM (FFA-CD) and the floorplanning algorithm with golden section strategy (FA-GSS) are proposed for the floorplanning problems with and without fixed-outline constraint. %FF-CD is committed to optimizing wirelength targets within a fixed profile. FA-GSS uses the Golden Section strategy to optimize both wirelength and area targets. The CSA is used to solve the proposed non-smooth optimization model, and the DEA-PPM is used to explore the module rotation scheme to enhance the flexibility of the algorithm. Numerical experiments on GSRC test circuits show that the proposed algorithms are superior to some celebrated B*-tree based floorplanning algorithms, and are expected to be applied to large-scale floorplanning problems due to their low time complexity.

We study policy optimization algorithms for computing correlated equilibria in multi-player general-sum Markov Games. Previous results achieve $O(T^{-1/2})$ convergence rate to a correlated equilibrium and an accelerated $O(T^{-3/4})$ convergence rate to the weaker notion of coarse correlated equilibrium. In this paper, we improve both results significantly by providing an uncoupled policy optimization algorithm that attains a near-optimal $\tilde{O}(T^{-1})$ convergence rate for computing a correlated equilibrium. Our algorithm is constructed by combining two main elements (i) smooth value updates and (ii) the optimistic-follow-the-regularized-leader algorithm with the log barrier regularizer., Comment: AISTATS 2024 Oral

Hybrid dynamical systems are ubiquitous as practical robotic applications often involve both continuous states and discrete switchings. Safety is a primary concern for hybrid robotic systems. Existing safety-critical control approaches for hybrid systems are either computationally inefficient, detrimental to system performance, or limited to small-scale systems. To amend these drawbacks, in this paper, we propose a learningenabled approach to construct local Control Barrier Functions (CBFs) to guarantee the safety of a wide class of nonlinear hybrid dynamical systems. The end result is a safe neural CBFbased switching controller. Our approach is computationally efficient, minimally invasive to any reference controller, and applicable to large-scale systems. We empirically evaluate our framework and demonstrate its efficacy and flexibility through two robotic examples including a high-dimensional autonomous racing case, against other CBF-based approaches and model predictive control.

We conducted an analysis of 45 bursts observed from 4U 1636$-$53. To investigate the mechanism behind the light curve profiles and the impact of thermonuclear X-ray bursts on the accretion environment in accreting neutron star low-mass X-ray binaries. This analysis employed both light curve and time-resolved spectroscopy methodologies, with data collected by the \textit{Insight}-HXMT instrument. We found that 30 bursts exhibited similar light curve profiles and were predominantly in the hard state, and two photospheric radius expansion (PRE) bursts were in the soft state. The light curves of most bursts did not follow a single exponential decay but displayed a dual-exponential behavior. The initial exponent had a duration of approximately 6 s. We utilized both the standard method and the `$f_{\rm a}$' method to fit the burst spectra. The majority of the `$f_{\rm a}$' values exceeded 1, indicating an enhancement of the persistent emission during the burst. Under the two comptonization components assumption, we suggest that the scattering of burst photons by the inner corona may mainly contribute to the persistent emission enhancement. We also observed an inverse correlation between the maximum $f_{\rm a}$ and the persistent emission flux in the non-PRE burst. This anti-correlation suggests that when the accretion rate is lower, there is a greater enhancement of persistent emission during the burst peak. The prediction based on Poynting-Robertson drag (P-R drag) aligns with this observed anti-correlation., Comment: accepted by MNRAS

In medical image diagnosis, fairness has become increasingly crucial. Without bias mitigation, deploying unfair AI would harm the interests of the underprivileged population and potentially tear society apart. Recent research addresses prediction biases in deep learning models concerning demographic groups (e.g., gender, age, and race) by utilizing demographic (sensitive attribute) information during training. However, many sensitive attributes naturally exist in dermatological disease images. If the trained model only targets fairness for a specific attribute, it remains unfair for other attributes. Moreover, training a model that can accommodate multiple sensitive attributes is impractical due to privacy concerns. To overcome this, we propose a method enabling fair predictions for sensitive attributes during the testing phase without using such information during training. Inspired by prior work highlighting the impact of feature entanglement on fairness, we enhance the model features by capturing the features related to the sensitive and target attributes and regularizing the feature entanglement between corresponding classes. This ensures that the model can only classify based on the features related to the target attribute without relying on features associated with sensitive attributes, thereby improving fairness and accuracy. Additionally, we use disease masks from the Segment Anything Model (SAM) to enhance the quality of the learned feature. Experimental results demonstrate that the proposed method can improve fairness in classification compared to state-of-the-art methods in two dermatological disease datasets.

We present an analytic calculation of the one-loop correction to the double-real emission contribution to the zero-jettiness soft function at N3LO in QCD, accounting for both gluon-gluon and quark-antiquark soft final-state partons. We explain all the relevant steps of the computation including the reduction of phase-space integrals to master integrals in the presence of Heaviside functions, and the methods we employed to compute them., Comment: 33 pages, results attached, v2: Normalization fixed, matches published version

The inherent irreversibility of quantum dynamics for open systems poses a significant barrier to the inversion of unknown quantum processes. To tackle this challenge, we propose the framework of virtual combs that exploit the unknown process iteratively with additional classical post-processing to simulate the process inverse. Notably, we demonstrate that an $n$-slot virtual comb can exactly reverse a depolarizing channel with one unknown noise parameter out of $n+1$ potential candidates, and a 1-slot virtual comb can exactly reverse an arbitrary pair of quantum channels. We further explore the approximate inversion of an unknown channel within a given channel set. A worst-case error decay of $\mathcal{O}(n^{-1})$ is unveiled for depolarizing channels within a specified noise region. Moreover, we show that virtual combs can universally reverse unitary operations and investigate the trade-off between the slot number and the sampling overhead., Comment: 5 + 14 pages, 3 figures

The lacunar spinel GaNb$_4$Se$_8$ is a tetrahedral cluster Mott insulator where spin-orbit coupling on molecular orbitals and Jahn-Teller energy scales are competitive. GaNb$_4$Se$_8$ undergoes a structural and anti-polar ordering transition at T$_Q$ = 50 K that corresponds to a quadrupolar ordering of molecular orbitals on Nb$_4$ clusters. A second transition occurs at T$_M$ = 29 K, where local distortions on the Nb$_4$ clusters rearrange. We present a single crystal x-ray diffraction investigation these phase transitions and solve the crystal structure in the intermediate T$_M$ < T < T$_Q$ and low T < T$_M$ temperature phases. The intermediate phase is a primitive cubic P2$_1$3 structure with a staggered arrangement of Nb4 cluster distortions. A symmetry mode analysis reveals that the transition at TQ is continuous and described by a single Jahn-Teller active amplitude mode. In the low temperature phase, the symmetry of Nb$_4$ clusters is further reduced and the unit cell doubles into an orthorhombic P2$_1$2$_1$2$_1$ space group. Nb$_4$ clusters rearrange through this transition to form a staggered arrangement of intercluster dimers, suggesting a valence bond solid magnetic state.

Table-based reasoning with large language models (LLMs) is a promising direction to tackle many table understanding tasks, such as table-based question answering and fact verification. Compared with generic reasoning, table-based reasoning requires the extraction of underlying semantics from both free-form questions and semi-structured tabular data. Chain-of-Thought and its similar approaches incorporate the reasoning chain in the form of textual context, but it is still an open question how to effectively leverage tabular data in the reasoning chain. We propose the Chain-of-Table framework, where tabular data is explicitly used in the reasoning chain as a proxy for intermediate thoughts. Specifically, we guide LLMs using in-context learning to iteratively generate operations and update the table to represent a tabular reasoning chain. LLMs can therefore dynamically plan the next operation based on the results of the previous ones. This continuous evolution of the table forms a chain, showing the reasoning process for a given tabular problem. The chain carries structured information of the intermediate results, enabling more accurate and reliable predictions. Chain-of-Table achieves new state-of-the-art performance on WikiTQ, FeTaQA, and TabFact benchmarks across multiple LLM choices., Comment: Accepted to ICLR 2024

Diffusion models have become the go-to method for large-scale generative models in real-world applications. These applications often involve data distributions confined within bounded domains, typically requiring ad-hoc thresholding techniques for boundary enforcement. Reflected diffusion models (Lou23) aim to enhance generalizability by generating the data distribution through a backward process governed by reflected Brownian motion. However, reflected diffusion models may not easily adapt to diverse domains without the derivation of proper diffeomorphic mappings and do not guarantee optimal transport properties. To overcome these limitations, we introduce the Reflected Schrodinger Bridge algorithm: an entropy-regularized optimal transport approach tailored for generating data within diverse bounded domains. We derive elegant reflected forward-backward stochastic differential equations with Neumann and Robin boundary conditions, extend divergence-based likelihood training to bounded domains, and explore natural connections to entropic optimal transport for the study of approximate linear convergence - a valuable insight for practical training. Our algorithm yields robust generative modeling in diverse domains, and its scalability is demonstrated in real-world constrained generative modeling through standard image benchmarks.

In the paper, we investigate the charmed meson rare decay process $D^+ \to \pi^+\nu\bar\nu$ by using QCD sum rules approach. Firstly, the pion twist-2 and twist-3 distribution amplitude $\xi$-moments $\langle\xi_{2;\pi}^n\rangle|_\mu$ up to 10th-order and $\langle \xi_{3;\pi}^{(p,\sigma),n}\rangle|_\mu$ up to fourth-order are calculated by using QCD sum rule under background field theory. After constructing the light-cone harmonic oscillator model for pion twist-2, 3 DAs, we get their behaviors by matching the calculated $\xi$-moments. Then, the $D\to \pi$ transition form factors are calculated by using QCD light-cone sum rules approach. The vector form factor at large recoil region is $f_+^{D\to\pi}(0) = 0.627^{+0.120} _{-0.080}$. By taking the rapidly $z(q^2,t)$ converging simplified series expansion, we present the TFFs and the corresponding angular coefficients in the whole squared momentum transfer physical region. Furthermore, we display the semileptonic decay process $\bar D^0 \to \pi^+ e\bar \nu_e$ differential decay widths and branching fraction with ${\cal B}(\bar D^0\to\pi^+e\bar\nu_e) = 0.308^{+0.155}_{-0.066} \times 10^{2}$. The $\bar D^0\to\pi^+e\bar\nu_e$ differential/total predictions for forward-backward asymmetry, $q^2$-differential flat terms and lepton polarization asymmetry are also given. After considering the non-standard neutrino interactions, the predictions for the $D^+ \to \pi^+ \nu\bar\nu$ branching fraction is ${\cal B}(D^+ \to \pi^+ {\nu }{\bar\nu}) = 1.85^{+0.93}_{-0.46}\times10^{-8}$., Comment: 12 pages, 9 figures