The main result of this note shows that there exists a sparse set in NP that is not in P if and only if EXPTIME≠NEXPTIME. Several other results are derived about the complexity of very sparse sets in NP–P and an interpretation of the meaning of these results is given in terms of ...
Though the main goal of this paper is to lay the foundations of two exact nonconvex reformulations of the sparse optimization problemSPO, the corresponding discussion leads, in a very natural way, to Lagrange–Newton-type methods for the solution ofSPO, see Sect.6. Like all Newton-type method...
The limitations of the method and the practical meaning of the sparsity assumption are discussed in section “Discussion and conclusions”. Source code for the algorithm presented as well as the url required to access updated versions of the code is included in the supplementary materials. ...
That causes the internal optimizations to be repeatedly created and destroyed in the `for` loop as well (meaning optimize_trsm timings will increase). Ideally we want the creation and destruction of the matrix handle (and if possible even the call to optimize_xxx() ...
For example, if j = 3, the range size is 2^3 = 8, meaning st[i][3] stores the result for the range [i, i + 7]. ### Building the Table We fill st[i][j] based on the idempotent property: st[i][j]=operation(st[i][j−1],st[i+2^j−1][j−1]) This...
We discuss the connectivity of the hard-disk sample space, the ergodicity of local MCMC algorithms, as well as the meaning of packings in the context of the NPT ensemble. Our work is accompanied by open-source, arbitrary-precision software for Böröczky packings (in Python) and for ...
Second, if Sn,λ≥ L, then the predictors are dense, meaning that there is no way to consistently estimate the relationship between all these predictors and the nth stock's returns in an L-minute estimation window no matter what approach you take. Either way, if the predictors are not ...
Adoption of high-content omic technologies in clinical studies, coupled with computational methods, has yielded an abundance of candidate biomarkers. However, translating such findings into bona fide clinical biomarkers remains challenging. To facilitate
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The accuracy level is set as \(5\%\), meaning the problem is considered solved if the solution is within \(5\%\) of the true answer. As dimensionality increases, our proposed DOSS algorithm can solve a greater number of problems to the given accuracy level. Furthermore, the superiority ...