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The Ceresa cycle is an algebraic 1-cycle on the Jacobian of an algebraic curve. Although it is homologically trivial, Ceresa famously proved that for a very general complex curve of genus at least 3, it is non-trivial in the Chow group. In this paper we study the Ceresa cycle attached to the complete modular curve $X_{0}(N)$. For prime level $p$ we give a complete description, namely we prove that if $X_{0}(p)$ is not hyperelliptic, then its Ceresa cycle is non-torsion. For general level $N$, we prove that there are finitely many $X_{0}(N)$ with torsion Ceresa cycle. Our method relies on the relationship between the vanishing of the Ceresa cycle and Chow-Heegner points on the Jacobian. We use the geometry and arithmetic of modular Jacobians to prove that such points are of infinite order and therefore deduce non-vanishing of the Ceresa cycle., Comment: comments welcome!

Automated reasoners, such as SAT/SMT solvers and first-order provers, are becoming the backbones of rigorous systems engineering, being used for example in applications of system verification, program synthesis, and cybersecurity. Automation in these domains crucially depends on the efficiency of the underlying reasoners towards finding proofs and/or counterexamples of the task to be enforced. In order to gain efficiency, automated reasoners use dedicated proof rules to keep proof search tractable. To this end, (variants of) subsumption is one of the most important proof rules used by automated reasoners, ranging from SAT solvers to first-order theorem provers and beyond. It is common that millions of subsumption checks are performed during proof search, necessitating efficient implementations. However, in contrast to propositional subsumption as used by SAT solvers and implemented using sophisticated polynomial algorithms, first-order subsumption in first-order theorem provers involves NP-complete search queries, turning the efficient use of first-order subsumption into a huge practical burden. In this paper we argue that the integration of a dedicated SAT solver opens up new venues for efficient implementations of first-order subsumption and related rules. We show that, by using a flexible learning approach to choose between various SAT encodings of subsumption variants, we greatly improve the scalability of first-order theorem proving. Our experimental results demonstrate that, by using a tailored SAT solver within first-order reasoning, we gain a large speedup in solving state-of-the-art benchmarks.

Graph neural networks (GNNs) have recently been adapted to temporal settings, often employing temporal versions of the message-passing mechanism known from GNNs. We divide temporal message passing mechanisms from literature into two main types: global and local, and establish Weisfeiler-Leman characterisations for both. This allows us to formally analyse expressive power of temporal message-passing models. We show that global and local temporal message-passing mechanisms have incomparable expressive power when applied to arbitrary temporal graphs. However, the local mechanism is strictly more expressive than the global mechanism when applied to colour-persistent temporal graphs, whose node colours are initially the same in all time points. Our theoretical findings are supported by experimental evidence, underlining practical implications of our analysis., Comment: 18 pages

The distribution of degree $d$ points on curves is well understood, especially for low degrees. We refine this study to include information on the Galois group in the simplest interesting case: $d = 3$. For curves of genus at least 5, we show cubic points with Galois group $C_3$ arise from well-structured morphisms, along with providing computable tests for the existence of such morphisms. We prove the same for curves of lower genus under some geometric or arithmetic assumptions., Comment: Comments welcome (14 pages)

We present the CheckMate tool for automated verification of game-theoretic security properties, with application to blockchain protocols. CheckMate applies automated reasoning techniques to determine whether a game-theoretic protocol model is game-theoretically secure, that is, Byzantine fault tolerant and incentive compatible. We describe CheckMate's input format and its various components, modes, and output. CheckMate is evaluated on 15 benchmarks, including models of decentralized protocols, board games, and game-theoretic examples.

Bjorn Poonen asked whether there exists a polynomial giving a surjection $\mathbb{Z} \times \mathbb{Z} \to \mathbb{N}$. We answer this question in the negative, conditional on a conjecture of Vojta. More precisely, we show that if such a function exists, there is a family of open surfaces with dense integral points despite the surfaces being of log general type., Comment: 11 pages, 1 figure. Comments welcome!

Classically, in saturation-based proof systems, unification has been considered atomic. However, it is also possible to move unification to the calculus level, turning the steps of the unification algorithm into inferences. For calculi that rely on unification procedures returning large or even infinite sets of unifiers, integrating unification into the calculus is an attractive method of dovetailing unification and inference. This applies, for example, to AC-superposition and higher-order superposition. We show that first-order superposition remains complete when moving unification rules to the calculus level. We discuss some of the benefits this has even for standard first-order superposition and provide an experimental evaluation., Comment: 16 pages, 0 figures, 1 table

Rewriting techniques based on reduction orderings generate "just enough" consequences to retain first-order completeness. This is ideal for superposition-based first-order theorem proving, but for at least one approach to inductive reasoning we show that we are missing crucial consequences. We therefore extend the superposition calculus with rewriting-based techniques to generate sufficient consequences for automating induction in saturation. When applying our work within the unit-equational fragment, our experiments with the theorem prover Vampire show significant improvements for inductive reasoning.

We develop an effective algorithm to compute the derivative of a Bianchi modular form with respect to weight space as it varies in a $p$-adic family. This method is entirely local at the modular form, and does not compute the family anywhere outside an infinitesimal neighbourhood. We numerically verify some conjectures surrouding smoothness of the eigenvariety (equivalently, uniqueness of families) and the ``direction over weight space'' of the family. The methods are also applied to study elliptic modular forms and their $\mathcal{L}$-invariants., Comment: 15 pages. Comments welcome!

We propose a new encoding of the first-order connection method as a Boolean satisfiability problem. The encoding eschews tree-like presentations of the connection method in favour of matrices, as we show that tree-like calculi have a number of drawbacks in the context of satisfiability solving. The matrix setting permits numerous global refinements of the basic connection calculus. We also show that a suitably-refined calculus is a decision procedure for the Bernays-Sch\"onfinkel class.

Subsumption resolution is an expensive but highly effective simplifying inference for first-order saturation theorem provers. We present a new SAT-based reasoning technique for subsumption resolution, without requiring radical changes to the underlying saturation algorithm. We implemented our work in the theorem prover Vampire, and show that it is noticeably faster than the state of the art.

In this paper we give an algorithm to find the 3-torsion subgroup of the Jacobian of a smooth plane quartic curve. We describe $3-$torsion points in terms of cubics which triply intersect the curve, and use this to define a system of equations whose solution set corresponds to the coefficients of these cubics. We compute the points of this zero-dimensional, degree $728$ scheme first by approximation, using homotopy continuation and Newton-Raphson, and then using lattice reduction or continued fractions to obtain accurate expressions for these points. We describe how the Galois structure of the field of definition of the $3$-torsion subgroup can be used to compute local conductor exponents, including at $p=2$., Comment: 18 pages, comments welcomed

Hyperspectral measurements from long range sensors can give a detailed picture of the items, materials, and chemicals in a scene but analysis can be difficult, slow, and expensive due to high spatial and spectral resolutions of state-of-the-art sensors. As such, sparsity is important to enable the future of spectral compression and analytics. It has been observed that environmental and atmospheric effects, including scattering, can produce nonlinear effects posing challenges for existing source separation and compression methods. We present a novel transformation into Hilbert spaces for pruning and constructing sparse representations via non-negative least squares minimization. Then we introduce max likelihood compression vectors to decrease information loss. Our approach is benchmarked against standard pruning and least squares as well as deep learning methods. Our methods are evaluated in terms of overall spectral reconstruction error and compression rate using real and synthetic data. We find that pruning least squares methods converge quickly unlike matching pursuit methods. We find that Hilbert space pruning can reduce error by as much as 40% of the error of standard pruning and also outperform neural network autoencoders.

There is increasing focus on analyzing data represented as hypergraphs, which are better able to express complex relationships amongst entities than are graphs. Much of the critical information about hypergraph structure is available only in the intersection relationships of the hyperedges, and so forming the "intersection complex" of a hypergraph is quite valuable. This identifies a valuable isomorphism between the intersection complex and the "concept lattice" formed from taking the hypergraph's incidence matrix as a "formal context": hypergraphs also generalize graphs in that their incidence matrices are arbitrary Boolean matrices. This isomorphism allows connecting discrete algorithms for lattices and hypergraphs, in particular s-walks or s-paths on hypergraphs can be mapped to order theoretical operations on the concept lattice. We give new algorithms for formal concept lattices and hypergraph s-walks on concept lattices. We apply this to a large real-world dataset and find deep lattices implying high interconnectivity and complex geometry of hyperedges.

Cryptographic protocols are hard to design and prove correct, as witnessed by the ever-growing list of attacks even on protocol standards. Symbolic models of cryptography enable automated formal security proofs of such protocols against an idealized model, which abstracts away from the algebraic properties of cryptographic schemes and thus misses attacks. Computational models yield rigorous guarantees but support at present only interactive proofs and/or restricted classes of protocols. A promising approach is given by the computationally complete symbolic attacker (CCSA), formalized in the BC Logic, which aims at bridging and getting the best of the two worlds, obtaining cryptographic guarantees by symbolic analysis. The BC Logic is supported by a recently developed interactive theorem prover, Squirrel, which enables machine-checked interactive security proofs, as opposed to automated ones, thus requiring expert knowledge. We introduce the CryptoVampire cryptographic protocol verifier, which for the first time fully automates proofs of trace properties in the BC Logic. The key technical contribution is a first-order (FO) formalization of protocol properties with tailored handling of subterm relations. We overcome the burden of interactive proving in higher-order (HO) logic and automatically establish soundness of cryptographic protocols using only FO reasoning. On the theoretical side, we restrict full FO logic with cryptographic axioms to ensure that, by losing the expressivity of the HO BC Logic, we do not lose soundness. On the practical side, CryptoVampire integrates dedicated proof techniques using FO saturation algorithms and heuristics, which enable leveraging the state-of-the-art Vampire FO theorem prover as the underlying proving engine. Our experimental results show CryptoVampire's effectiveness of as a standalone verifier and in terms of automation support for Squirrel.

Linear neural network layers that are either equivariant or invariant to permutations of their inputs form core building blocks of modern deep learning architectures. Examples include the layers of DeepSets, as well as linear layers occurring in attention blocks of transformers and some graph neural networks. The space of permutation equivariant linear layers can be identified as the invariant subspace of a certain symmetric group representation, and recent work parameterized this space by exhibiting a basis whose vectors are sums over orbits of standard basis elements with respect to the symmetric group action. A parameterization opens up the possibility of learning the weights of permutation equivariant linear layers via gradient descent. The space of permutation equivariant linear layers is a generalization of the partition algebra, an object first discovered in statistical physics with deep connections to the representation theory of the symmetric group, and the basis described above generalizes the so-called orbit basis of the partition algebra. We exhibit an alternative basis, generalizing the diagram basis of the partition algebra, with computational benefits stemming from the fact that the tensors making up the basis are low rank in the sense that they naturally factorize into Kronecker products. Just as multiplication by a rank one matrix is far less expensive than multiplication by an arbitrary matrix, multiplication with these low rank tensors is far less expensive than multiplication with elements of the orbit basis. Finally, we describe an algorithm implementing multiplication with these basis elements., Comment: Comments welcome!

Noting that lemmas are a key feature of mathematics, we engage in an investigation of the role of lemmas in automated theorem proving. The paper describes experiments with a combined system involving learning technology that generates useful lemmas for automated theorem provers, demonstrating improvement for several representative systems and solving a hard problem not solved by any system for twenty years. By focusing on condensed detachment problems we simplify the setting considerably, allowing us to get at the essence of lemmas and their role in proof search., Comment: Extended version of the TABLEAUX 2023 contribution

Concurrent programming is used in all large and complex computer systems. However, concurrency errors and system failures (ex: crashes and deadlocks) are common. We find that Petri nets can be used to model concurrent systems and find and remove errors ahead of time. We introduce a novel generalization of Petri nets with nondeterministic transition nodes to match real systems. These allow for a compact way to construct, optimize, and prove computer programs at the concurrency level. Petri net programs can also be optimized by automatically solving for maximal concurrency, where the maximum number of valid threads is determined by the structure of the Petri net prior to execution. We discuss an algorithm to compute the state graph of a given Petri net start state pair. We introduce our open source software framework which implements this theory as a general purpose concurrency focused middle-ware.

It is known that for a curve defined over $\mathbb{Q}$ of genus $g \leq 4$, there exists a point on the curve defined over a solvable extension of $\mathbb{Q}$. We relate points on curves of genus $g \geq 5$ over solvable extensions to the Bombieri-Lang conjecture. Specifically, it shows that varieties parameterising points defined over extensions with a fixed solvable Galois group are of general type. Moreover, we show the existence of certain subvarieties in these varieties imply the existence of solvable morphisms from the curve.

Purpose To develop and evaluate a deep learning-based method (MC-Net) to suppress motion artifacts in brain magnetic resonance imaging (MRI). Methods MC-Net was derived from a UNet combined with a two-stage multi-loss function. T1-weighted axial brain images contaminated with synthetic motions were used to train the network. Evaluation used simulated T1 and T2-weighted axial, coronal, and sagittal images unseen during training, as well as T1-weighted images with motion artifacts from real scans. Performance indices included the peak signal to noise ratio (PSNR), structural similarity index measure (SSIM), and visual reading scores. Two clinical readers scored the images. Results The MC-Net outperformed other methods implemented in terms of PSNR and SSIM on the T1 axial test set. The MC-Net significantly improved the quality of all T1-weighted images (for all directions and for simulated as well as real motion artifacts), both on quantitative measures and visual scores. However, the MC-Net performed poorly on images of untrained contrast (T2-weighted). Conclusion The proposed two-stage multi-loss MC-Net can effectively suppress motion artifacts in brain MRI without compromising image context. Given the efficiency of the MC-Net (single image processing time ~40ms), it can potentially be used in real clinical settings. To facilitate further research, the code and trained model are available at https://github.com/MRIMoCo/DL_Motion_Correction.

Artificial intelligence (AI) assisting with antimicrobial prescribing raises significant moral questions. Utilising ethical frameworks alongside AI-driven systems, while considering infection specific complexities, can support moral decision making to tackle antimicrobial resistance.

Antimicrobial resistance (AMR) is a growing public health threat, estimated to cause over 10 million deaths per year and cost the global economy 100 trillion USD by 2050 under status quo projections. These losses would mainly result from an increase in the morbidity and mortality from treatment failure, AMR infections during medical procedures, and a loss of quality of life attributed to AMR. Numerous interventions have been proposed to control the development of AMR and mitigate the risks posed by its spread. This paper reviews key aspects of bacterial AMR management and control which make essential use of data technologies such as artificial intelligence, machine learning, and mathematical and statistical modelling, fields that have seen rapid developments in this century. Although data technologies have become an integral part of biomedical research, their impact on AMR management has remained modest. We outline the use of data technologies to combat AMR, detailing recent advancements in four complementary categories: surveillance, prevention, diagnosis, and treatment. We provide an overview on current AMR control approaches using data technologies within biomedical research, clinical practice, and in the "One Health" context. We discuss the potential impact and challenges wider implementation of data technologies is facing in high-income as well as in low- and middle-income countries, and recommend concrete actions needed to allow these technologies to be more readily integrated within the healthcare and public health sectors., Comment: 65 pages, 3 figures

Large neural networks are heavily over-parameterized. This is done because it improves training to optimality. However once the network is trained, this means many parameters can be zeroed, or pruned, leaving an equivalent sparse neural network. We propose renormalizing sparse neural networks in order to improve accuracy. We prove that our method's error converges to zero as network parameters cluster or concentrate. We prove that without renormalizing, the error does not converge to zero in general. We experiment with our method on real world datasets MNIST, Fashion MNIST, and CIFAR-10 and confirm a large improvement in accuracy with renormalization versus standard pruning.

Persistent homology is a crucial invariant that is used in many areas to understand data. The $O(N^4)$ run time is a hindrance to its use on most large datasets. We give a parallelization method to utilize multi-core machines and clusters. We implement the computation of the $0^{th}$ persistent homology with OpenMP parallelization and observe a 1.75 fold performance increase by using 2 threads on a dual core machine. We also benchmark the computation using larger numbers of threads and show that the thread computational overhead decreases performance. With GPU parallelization, we analytically and empirically decrease the run time scaling from $O(N^4)$ to $O(N^3)$ and even $O(N^2)$ where $N$ is the number of data points, for a large enough GPU. Next, we analytically show run time scaling $O(N)$ for an even larger GPU.

We develop and test a novel unsupervised algorithm for word sense induction and disambiguation which uses topological data analysis. Typical approaches to the problem involve clustering, based on simple low level features of distance in word embeddings. Our approach relies on advanced mathematical concepts in the field of topology which provides a richer conceptualization of clusters for the word sense induction tasks. We use a persistent homology barcode algorithm on the SemCor dataset and demonstrate that our approach gives low relative error on word sense induction. This shows the promise of topological algorithms for natural language processing and we advocate for future work in this promising area.

Brain function and connectivity is a pressing mystery in medicine related to many diseases. Neural connectomes have been studied as graphs with graph theory methods including topological methods. Work has started on hypergraph models and methods where the geometry and topology is significantly different. We define a hypergraph called the hyper-connectome with joint information entropy and total correlation. We give the pseudocode for computation from finite samples. We give the theoretic importance of this generalization's topology and geometry with respect to random variables and then prove the hypergraph can be necessary for prediction and classification. We confirm with a simulation study and computation. We prove the approximation for continuous random variables with finite samples. We compare connectome versus hyper-connectome for predicting schizophrenia in subjects based on a fMRI dataset using a linear support vector machine. The hyper-connectome achieves better performance in accuracy (up to 56\%) and F1 score (up to 0.52) than the connectome. We reject null hypothesis at 95\% with p-value = 0.00074.

Super resolution is an essential tool in optics, especially on interstellar scales, due to physical laws restricting possible imaging resolution. We propose using optimal transport and entropy for super resolution applications. We prove that the reconstruction is accurate when sparsity is known and noise or distortion is small enough. We prove that the optimizer is stable and robust to noise and perturbations. We compare this method to a state of the art convolutional neural network and get similar results for much less computational cost and greater methodological flexibility., Comment: 5 pages, 2 figures

In today's technology environment, information is abundant, dynamic, and heterogeneous in nature. Automated filtering and prioritization of information is based on the distinction between whether the information adds substantial value toward one's goal or not. Contextual multi-armed bandit has been widely used for learning to filter contents and prioritize according to user interest or relevance. Learn-to-Rank technique optimizes the relevance ranking on items, allowing the contents to be selected accordingly. We propose a novel approach to top-K rankings under the contextual multi-armed bandit framework. We model the stochastic reward function with a neural network to allow non-linear approximation to learn the relationship between rewards and contexts. We demonstrate the approach and evaluate the the performance of learning from the experiments using real world data sets in simulated scenarios. Empirical results show that this approach performs well under the complexity of a reward structure and high dimensional contextual features.

Policy learning is a quickly growing area. As robotics and computers control day-to-day life, their error rate needs to be minimized and controlled. There are many policy learning methods and bandit methods with provable error rates that accompany them. We show an error or regret bound and convergence of the Deep Epsilon Greedy method which chooses actions with a neural network's prediction. We also show that Epsilon Greedy method regret upper bound is minimized with cubic root exploration. In experiments with the real-world dataset MNIST, we construct a nonlinear reinforcement learning problem. We witness how with either high or low noise, some methods do and some do not converge which agrees with our proof of convergence.

Contextual multi-armed bandits (CMAB) have been widely used for learning to filter and prioritize information according to a user's interest. In this work, we analyze top-K ranking under the CMAB framework where the top-K arms are chosen iteratively to maximize a reward. The context, which represents a set of observable factors related to the user, is used to increase prediction accuracy compared to a standard multi-armed bandit. Contextual bandit methods have mostly been studied under strict linearity assumptions, but we drop that assumption and learn non-linear stochastic reward functions with deep neural networks. We introduce a novel algorithm called the Deep Upper Confidence Bound (UCB) algorithm. Deep UCB balances exploration and exploitation with a separate neural network to model the learning convergence. We compare the performance of many bandit algorithms varying K over real-world data sets with high-dimensional data and non-linear reward functions. Empirical results show that the performance of Deep UCB often outperforms though it is sensitive to the problem and reward setup. Additionally, we prove theoretical regret bounds on Deep UCB giving convergence to optimality for the weak class of CMAB problems.

In this paper we consider the decomposition of positive semidefinite matrices as a sum of rank one matrices. We introduce and investigate the properties of various measures of optimality of such decompositions. For some classes of positive semidefinite matrices we give explicitly these optimal decompositions. These classes include diagonally dominant matrices and certain of their generalizations, $2\times 2$, and a class of $3\times 3$ matrices., Comment: Will appear in a Springer book "Harmonic Analysis and Applications", Ed. M. Rassias

The "Square Kilometre Array" (SKA) is a large international radio telescope project characterised, as suggested by its name, by a total collecting area of approximately one square kilometre, and consisting of several interferometric arrays to observe at metric and centimetric wavelengths. The deployment of the SKA will take place in two sites, in South Africa and Australia, and in two successive phases. From its Phase 1, the SKA will be one of the most formidable scientific machines ever deployed by mankind, and by far the most impressive in terms of data throughput and required computing power. With the participation of almost 200 authors from forty research institutes and six private companies, the publication of this French SKA white paper illustrates the strong involvement in the SKA project of the French astronomical community and of a rapidly growing number of major scientific and technological players in the fields of Big Data, high performance computing, energy production and storage, as well as system integration., Comment: Editor in chief: C. Ferrari; Editors: M. Alves, S. Bosse, S. Corbel, A. Ferrari, K. Ferri\`ere, S. Gauffre, E. Josselin, G. Lagache, S. Lambert, G. Marquette, J.-M. Martin, M.-A. Miville-Desch\^enes, L. Montier, B. Semelin, G. Theureau, S. Vergani, N. Vilmer, P. Zarka; Original file with high resolution figures at SKA-France link: https://ska-france.oca.eu/images/SKA-France-Media/FWB_051017.pdf

We report on the discovery of Cepheids in the Virgo spiral galaxy NGC 4535, based on observations made with the Wide Field and Planetary Camera 2 on board the Hubble Space Telescope. NGC 4535 is one of 18 galaxies observed as a part of The HST Key Project on the Extragalactic Distance Scale which aims to measure the Hubble constant to 10% accuracy. NGC 4535 was observed over 13 epochs using the F555W filter, and over 9 epochs using the F814W filter. The HST F555W and F814W data were transformed to the Johnson V and Kron-Cousins I magnitude systems, respectively. Photometry was performed using two independent programs, DoPHOT and DAOPHOT II/ALLFRAME. Period-luminosity relations in the V and I bands were constructed using 39 high-quality Cepheids present in our set of 50 variable candidates. We obtain a distance modulus of 31.02+/-0.26 mag, corresponding to a distance of 16.0+/-1.9 Mpc. Our distance estimate is based on values of mu = 18.50 +/- 0.10 mag and E(V-I) = 0.13 mag for the distance modulus and reddening of the LMC, respectively., Comment: Accepted for publication in the Astrophysical Journal. 22 pages of text, 22 pages of tables and 11 figures. ASCII tables and PostScript versions of all figures available at http://www.ipac.caltech.edu/H0kp

We report the detection of Cepheid variable stars in the barred spiral galaxy NGC 1365, located in the Fornax cluster, using the Hubble Space Telescope Wide Field and Planetary Camera 2. Twelve V (F555W) and four I (F814W) epochs of observation were obtained. The two photometry packages, ALLFRAME and DoPHOT, were separately used to obtain profile-fitting photometry of all the stars in the HST field. The search for Cepheid variable stars resulted in a sample of 52 variables, with periods between 14 and 60 days, in common with both datasets. ALLFRAME photometry and light curves of the Cepheids are presented. A subset of 34 Cepheids were selected on the basis of period, light curve shape, similar ALLFRAME and DoPHOT periods, color, and relative crowding, to fit the Cepheid period-luminosity relations in V and I for both ALLFRAME and DoPHOT. The measured distance modulus to NGC 1365 from the ALLFRAME photometry is 31.31 +/- 0.20 (random) +/- 0.18 (systematic) mag, corresponding to a distance of 18.3 +/- 1.7 (random) +/- 1.6 (systematic) Mpc. The reddening is measured to be E(V-I) = 0.16 +/- 0.08 mag. These values are in excellent agreement with those obtained using the DoPHOT photometry, namely a distance modulus of 31.26 +/- 0.10 mag, and a reddening of 0.15 +/- 0.10 mag (internal errors only)., Comment: 48 pages, 8 tables, 8 figures, to appear in ApJ

Uncertainty in the metal abundance dependence of the Cepheid variable period- luminosity (PL) relation remains one of the outstanding sources of systematic error in the extragalactic distance scale and Hubble constant. To test for such a metallicity dependence, we have used the WFPC2 camera on the Hubble Space Telescope (HST) to observe Cepheids in two fields in the nearby spiral galaxy M101, which span a range in oxygen abundance of 0.7+-0.15 dex. A differential analysis of the PL relations in V and I in the two fields yields a marginally significant change in the inferred distance modulus on metal abundance, with d(m-M)/d[O/H] = -0.24+-0.16 mag/dex. The trend is in the theoretically predicted sense that metal-rich Cepheids appear brighter and closer than metal-poor stars. External comparisons of Cepheid distances with those derived from three other distance indicators, in particular the tip of the red giant branch method, further constrain the magnitude of any Z-dependence of the PL relation at V and I. The overall effects of any metallicity dependence on the distance scale derived with HST will be of the order of a few percent or less for most applications, though distances to individual galaxies at the extremes of the metal abundance range may be affected at the 10% level., Comment: 28 pages, 4 tables, 10 figures, to appear in The Astrophysical Journal

We report on the discovery of Cepheids in the field spiral galaxy NGC 3621, based on observations made with the Wide Field and Planetary Camera 2 on board the Hubble Space Telescope (HST). NGC 3621 is one of 18 galaxies observed as a part of The HST Key Project on the Extragalactic Distance Scale, which aims to measure the Hubble constant to 10% accuracy. Sixty-nine Cepheids with periods in the range 9--60 days were observed over 12 epochs using the F555W filter, and 4 epochs using the F814W filter. The HST F555W and F814W data were transformed to the Johnson V and Kron-Cousins I magnitude systems, respectively. Photometry was performed using two independent packages, DAOPHOT II/ALLFRAME and DoPHOT. Period-luminosity relations in the V and I bands were constructed using 36 fairly isolated Cepheids present in our set of 69 variables. Extinction-corrected distance moduli relative to the LMC of 10.63 +/- 0.07 mag and 10.56 +/- 0.10 mag were obtained using the ALLFRAME and DoPHOT data, respectively. True distance moduli of 29.13 +/- 0.18 mag and 29.06 +/- 0.18 mag, corresponding to distances of 6.3 Mpc and 6.1 Mpc, were obtained by assuming values of 18.50 +/- 0.10 mag for the distance modulus of the LMC and E(V-I) = 0.13 mag for the reddening of the LMC., Comment: 29 pages, 13 tables, 36 figures, accepted for publication in ApJ. LaTeX, uses aasms.sty and apjpt4.sty Key Project archive at http://www.ipac.caltech.edu/H0kp

The use of Artificial Neural Networks (ANNs) as a classifier of digital spectra is investigated. Using both simulated and real data, it is shown that neural networks can be trained to discriminate between the spectra of different classes of active galactic nucleus (AGN) with realistic sample sizes and signal-to-noise ratios. By working in the Fourier domain, neural nets can classify objects without knowledge of their redshifts., Comment: 11 pages, LaTeX, including two postscript figures, 41 kb. Accepted for publication in Publ. ASA

A research project conducted from July 1974 through June 1976 to develop more comprehensive State-local planning for curriculum development, work-experience programs, and programs for the disadvantaged and handicapped was designed to coordinate total planning activities from the Kansas State Department of Education to the local classroom level. A regional service unit was established to serve nine counties in economically depressed southeast Kansas and a needs assessment was made to determine educational shortcomings. Manpower needs data were gathered from employers in the nine-county area, as well as data on vocational curriculum interests from students, parents, and school staffs. Study findings revealed that educators at all levels and many area employers were actively involved in the project. As a result of regional cooperative planning local schools increased their proposals for innovative projects, inservice training needs were pinpointed, and the role of career education in all aspects of education was demonstrated. The regional service unit conducted inservice workshops on career and special education and on vocational curriculum development. Study findings are detailed in the report, and materials related to the occupational survey, inservice workshops, evaluation, and proposed plans are appended. (MF)

Compares responses on self-report inventories of coping resources and self-esteem between samples of students attending a small private college and a large state university. Differences were found in physical and spiritual/philosophical types of coping resources as well as social self-esteem. Includes suggestions for further research in this area along with implications for effective student affairs programming. (Contains 25 references and 3 tables.) (Author/GCP)

The final report, covering the time period from January 1, 1971 to June 30, 1973, summarizes an exemplary program to introduce career education into three Kansas project sites: Kansas City, Clay Center, and Lawrence, which are representative of the schools in the State. Individual reports from the project sites and from the cooperating State university are included. Goals and objectives, procedures, results and accomplishments, and an internal evaluation are detailed. Recommendations concern funding, teacher training, curriculum revision, job entry training, counseling, provisions for added evaluative devices, and added dissemination of career education to students, parents, and community. (MU)

The K-8 career education project (Jan. 1, 1972-Aug. 1, 1973) was intended to establish a demonstration testing and development model of career education in a consortium of 18 rural school districts participating in the Unified Schools Association for Vocational Education (USA-VE) organization, encompassing nine counties in northwest Kansas. The project focused on two major phases of inservice teacher education: (1) the formalized inservice training of administrators, counselors, and teachers; and (2) the informalized continuing inservice education of teachers using visiting career awareness assistants and mobile media centers. The report briefly covers: the need for the project, the project's goals and objectives expressed as teacher outcomes, the procedures followed in setting up administrator workshops and inservice teacher education and workshops, selection and utilization of media and instructional materials, developing a handbook for teachers, advisory council operation, information dissemination, and the project's results and conclusions. Concluding the document are four appendixes: USA-VE Unified School Districts' population characteristics, a Career Significance Study questionnaire for teachers, a parental survey form, and an employer survey form. (BP)