Descent Path Research Articles

A holistic lens on entrepreneurial learning from failure: continuing the legacy of Jason Cope

PurposeThe paper follows Jason Cope's (2011) vision of a holistic perspective on the failure-based learning process. By analyzing the research since Cope's first attempt, which is often fragmentary in nature, and providing novel empirical insights, the paper aims to draw a new comprehensive picture of all five phases of entrepreneurial learning and their interplay.Design/methodology/approachThe study features an interpretative phenomenological analysis of in-depth interviews with 18 failed entrepreneurs. Findings are presented and discussed in line with experiential learning theory and Cope's conceptual framework of five interrelated learning timeframes spanning from the descent into failure until re-emergence.FindingsThe study reveals different patterns of how entrepreneurs experience failure, ranging from abrupt to gradual descent paths, different management and coping behaviors, and varying learning effects depending on the new professional setting (entrepreneurial vs non-entrepreneurial). Analyzing the entrepreneurs' experiences throughout the process shows different paths and connections between individual phases. Findings indicate that the learning timeframes may overlap, appear in different orders, loop, or (partly) stay absent, indicating that the individual learning process is even more dynamic and heterogeneous than hitherto known.Originality/valueThe paper contributes to the field of entrepreneurial learning from failure, advancing Cope's seminal work on the learning process and -contents by providing novel empirical insights and discussing them in the light of recent scientific findings. Since entrepreneurial learning from failure is a complex and dynamic process, using a holistic lens in the analysis contributes to a better understanding of this phenomenon as an integrated whole.

Pseudo-Jahn-Teller effect in deprotonated dimethyl amino phenyl substituted phthalocyanine

Geometries of dimethyl amino phenyl substituted phtalocyanine deprotonated at two nitrogen atoms [dmaphPc]q, q = -2, -1 and 0, were optimized within the D4h symmetry group and its subgroups. Their excited states were evaluated using the TD-DFT treatment. Using an epikernel principle method based on the symmetries of the imaginary vibrations of the optimized geometries and the symmetries of the corresponding excited states, the symmetry descent paths D4h → D4 for [dmaphPc]2-, D4h → D2 for [dmaphPc]−, and D4h → C2 for [dmaphPc]0 were explained as a consequence of the pseudo-Jahn-Teller effect.

Logarithmic singularity subtraction for matrix‐friendly layered medium Green's functions

AbstractA subtraction procedure is proposed to evaluate the logarithmic singularity for matrix‐friendly layered medium Green's functions. In this subtraction procedure, an integral of the Bessel function combined with the exponential function and power function, where the sum of the power of and the order of the Bessel function is −1, is designed to fit the oscillation of the tail integral. After subtracting the designed integral, the integrand of the remainder decreases rapidly. Accordingly, the remainder can be calculated without finding any surface poles or steepest descent path, while the subtracted part can be calculated analytically. Several numerical examples are provided to reveal the feasibility and the accuracy of the proposed method.

Optical design algorithm utilizing continuous-discrete variables grounded on stochastic processes

This work proposes an optimization algorithm in optical design based on the concepts of ergodic and stochastic processes in statistical mechanics. In mixed-variable optimization problems, pseudo-random number and discrete-to-continuous variable conversion dramatically increase the speed at which the system solves for the optimal solution. Pseudo-random numbers are mainly applied in two important steps in the optimization algorithm: determining the combination of glasses involved and the order in which the successive glass parameters are replaced by real glasses. After two series of stochastic processes, the merit function value decreases rapidly along the steepest descent path, and thus the optical system approaches the optimal solution within a very short duration of time. By using the method proposed in this paper, a plan apochromatic objective with a long working distance was optimized, and finally, a high-quality optical system was obtained.

A novel multi-gradient evolutionary deep learning approach for few-shot wind power prediction using time-series GAN

Due to the lack of historical data, accurate prediction is a great challenge for newly constructed wind farms (NWFs). How to guarantee satisfactory prediction accuracy with limited data has become a bottleneck issue in wind power prediction (WPP). To solve the few-shot learning problem in NWFs, a novel multi-gradient evolutionary deep learning neural network (EATDLNN) prediction model is proposed, which incorporates the time-series GAN (TimeGAN) and multivariate variational mode decomposition (MVMD) method. TimeGAN adds an auto-encoder network and a supervised loss function to GAN, which enables it to capture the dynamic time series correlation characteristics of wind data and generate high-quality samples. MVMD is then employed to simultaneously decompose nonstationary sequences. In the EATDLNN prediction model, an evolution-based multi-gradient training approach is proposed to train the DLNN by integrating three gradient descent methods (i.e., Adam, MBGD-Momentum, RMSprop). Compared with the traditional single-gradient training approach, the multi-gradient training approach provides different gradient descent paths and the gradient can adaptively choose to update towards the path with the smallest error based on the evolutionary framework, which can help the model jump out of the local optimum and enhance the generalization ability. Massive experiments prove the excellent performance of the proposed method, especially in one-step prediction, the root mean square errors reduce by 79.40%∼91.05% compared with other state-of-the-art methods.

Lunar descent and landing via two-phase explicit guidance and pulse-modulated reduced-attitude control

This work considers the three-dimensional descent path of a space vehicle, from periselenium of its operational orbit to the lunar surface. The trajectory is split in two arcs: (1) descent path, up to an altitude of 50 m, and (2) terminal approach and soft touchdown. For phase 1, a new, three-dimensional locally-flat near-optimal guidance is introduced that is based on the local projection of the position and velocity variables. A minimum-time problem is defined using the locally flat coordinates of position and velocity. This leads to identifying closed-form functions of time for the two thrust angles, which identify the commanded thrust direction. During terminal approach (phase 2), correct vertical alignment, modest velocity, and negligible angular rate at touchdown are pursued. With this intent, a predictive bang-off-bang guidance algorithm is proposed that is capable of guaranteeing the desired final conditions. In both phases, the attitude control system has the objective of aligning the actual thrust direction with the commanded one, provided by the guidance algorithm. The resulting reduced-attitude control problem is addressed through the use of a new quaternion-based nonlinear control algorithm, which is proven to enjoy asymptotic stability properties. The attitude actuation system is composed of 12 monopropellant thrusters, ignited using pulse width modulation. Monte Carlo simulations are run, assuming significant displacements from the nominal initial conditions and including several harmonics of the selenopotential. The numerical results unequivocally prove that the guidance and control architecture proposed in this study is effective to achieve lunar descent and safe touchdown in nonnominal flight conditions.

Complete Nonuniform Asymptotic Expansion of Sommerfeld Integral for Dielectric Half-Space

Generally, the Sommerfeld integral (SI) for a dielectric half-space is approximated based on the steepest descent method. A higher order approximation of the integral requires higher order derivatives of the integrand in the steepest descent path in the complex domain, whose explicit formulation may be cumbersome. Recently, a new finite-range integral representation of the SI has been proposed, whose integrand is written in terms of the SI for an impedance half-plane. Based on the known complete nonuniform asymptotic expansion of the SI for an impedance half-plane, the complete nonuniform asymptotic expansion can be analytically formulated for the dielectric half-space. Moreover, the completeness is mathematically proven such that the expansion satisfies the recurrence relation for the Wilcox expansion. The accuracy of the proposed expansion is numerically examined for several propagation scenarios. Furthermore, a numerical procedure is proposed to calculate the higher order terms of the expansion by partially using the impedance approximation for a large relative permittivity of the half-space.

Brachistochrone Curve Representation via Transition Curve

The brachistochrone curve is an optimal curve that allows the fastest descent path of an object to slide frictionlessly under the influence of a uniform gravitational field. In this paper, the Brachistochrone curve will be reconstructed using two different basis functions, namely Bézier curve and trigonometric Bézier curve with shape parameters. The Brachistochrone curve between two points will be approximated via a C-shape transition curve. The travel time and curvature will be evaluated and compared for each curve. This research revealed that the trigonometric Bézier curve provides the closest approximation of Brachistochrone curve in terms of travel time estimation, and shape parameters in trigonometric Bézier curve provide better shape adjustability than Bézier curve.

Air-to-Ground Cellular Communications for Airplane Maintenance Data Offloading

Airplane sensors and on-board equipment collect an increasingly large amount of maintenance data during flights that are used for airplane maintenance. We propose to download part of the data during airplane’s descent via a cellular base station (BS) located at the airport. We formulate and solve an offline optimization problem to quantify how much data can be offloaded in a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">non-dedicated band</i> while ensuring that the interference power at the terrestrial BSs in the vicinity of the airport remains below a maximum allowable threshold. Our problem allows for adaptive tuning of transmit power, number of frequency channels to be used, and beamforming according to the position of the plane on the descent path. Our results show that, when the BS at the airport and the plane are equipped with uniform planar arrays, during the last 5 minutes of descent, in the microwave band the plane can offload up to 5GB of maintenance data in a 20 MHz band with a transmit power of 1 W or 40 W. In the mmWave band, the plane can offload up to 24 times more data in a 1 GHz band, with a transmit power of 40 W (using most of the bandwidth) and below 4 times with a transmit power of 1 W (effectively using a maximum of 202 MHz due to bandwidth tuning). Beamforming, power and bandwidth tuning are all crucial in maintaining a good performance in the mmWave band while in the microwave band, dynamic tuning of bandwidth does not improve the performance noticeably.

An analysis of the steepest descent method to efficiently compute the three-dimensional acoustic single-layer operator in the high-frequency regime

Abstract Using the Cauchy integral theorem, we develop the application of the steepest descent method to efficiently compute the three-dimensional acoustic single-layer integral operator for large wave numbers. Explicit formulas for the splitting points are derived in the one-dimensional case to build suitable complex integration paths. The construction of admissible steepest descent paths is next investigated and some of their properties are stated. Based on these theoretical results, we derive the quadrature scheme of the oscillatory integrals first in dimension one and then extend the methodology to three-dimensional planar triangles. Numerical simulations are finally reported to illustrate the accuracy and efficiency of the proposed approach.

Explicit Near-Optimal Guidance and Pulse-Modulated Control for Lunar Descent and Touchdown

This research considers the descent path of a space vehicle, from periselenium of its operational orbit to the lunar surface. The trajectory is split in two arcs: (a) approach, up to a specified altitude, and (b) terminal descent and soft touchdown. For phase (a), a new locally flat near-optimal guidance is used, which is based on iterative projection of the spacecraft position and velocity, and availability of closed-form expressions for the related costate variables. Attitude control is aimed at pursuing the desired spacecraft orientation, and uses an adaptive tracking scheme that compensates for the inertia uncertainties. Arc (b) is aimed at gaining the correct vertical alignment and low velocity at touchdown. For phase (b) a predictive bang-off-bang guidance algorithm is proposed that is capable of guaranteeing the desired final conditions, while providing the proper allocation of side jet ignitions. Actuation of side jets is implemented using pulse width modulation, in both phases. Monte Carlo simulations prove that the guidance and control architecture at hand drives the spacecraft toward safe touchdown, in the presence of non-nominal flight conditions.

Computing saddle graphs via homotopy continuation for the approximate synthesis of mechanisms

An approach for approximate kinematic synthesis of mechanisms is proposed in this paper which computes a graph that identifies minima of an objective function as vertices and connections between them as edges. Such a graph is interactively presented to a designer, whereby edges are continuously traversed to navigate families of design candidates in between minima. Candidates are evaluated continuously according to auxiliary considerations for the exploration of design trade-offs. Relevant design specifications tend to be particular per application and are either unclear as how to incorporate into an objective, or clear but with great consequence to the complexity of function evaluation. Computing the aforementioned graphs begins with finding all minima and saddles of an objective function through polynomial homotopy continuation. Connections between minima that minimize their maximum objective value must pass through a saddle to do so. Therefore, after gathering saddles, each is perturbed both ways in its least eigendirection to seed gradient descent paths which connect two minima when pieced together. Discovered connections between minima are organized into a graph, where edges correspond to gradient descent paths.

Sliding mode controller based aircraft automatic landing for alternate profiles

In the present paper, different autonomous landing profiles are formulated and simulated. Generic landing is modelled first, wherein, approach and acquired runway heading is considered as same. The second-landing profile involves altitude hold when runway is not clear to land the aircraft. Expedited landing is the third profile modelled with a glide slope-maintained descent to reduce the ground distance required pre-touchdown. In either of the landing profiles, flare is kept the same. The merits and demerits with respect to the practicality of implementation of these profiles are then discussed. Each landing profile has been demonstrated using sliding mode controller (SMC). The asymptotic stability and finite-time proofs of the designed controller are shown using Lyapunov function. F-18 HARV aircraft is considered to test the efficacy of the formulated landing profiles. Expedited landing profile proposed here is a novel approach in which altitude descent gradient is maintained with helical descent path. Additionally, results of this approach show significant improvement in terms of possibility of initiating an unconventional and yet safe as well as economical method much nearer to the runway.

On the Near-Field Spherical Wave Formation in Resonant Leaky-Wave Antennas: Application to Small Lens Design

In this work, we show that the near field of leaky-wave resonant antennas (LWAs) radiating into a dense medium can be locally represented as a spherical wave in a certain solid angle around broadside using an accurate definition of the phase center. The near field in this solid angle can be efficiently evaluated through the integration of the spectral Green’s function along the steepest descent path (SDP). Beyond this solid angle, defined as the shadow boundary angle, a residual contribution due to the leaky-wave pole must also be added to fully describe the near field. It is found that this shadow boundary angle can be used to define the phase center and geometry of a truncated lens that couples well to leaky-wave antennas, even in electrically small-to-medium sized lenses and low-contrast cases. To demonstrate the applicability of the proposed study, we combine the SDP field calculation with a Fourier optics (FO) methodology to evaluate the aperture efficiency and radiation patterns of small-to-medium sized lenses in reception. A truncated silicon lens with a diameter of only four free-space wavelengths is presented with almost 80% aperture efficiency. Excellent agreement with full-wave simulations is achieved, which demonstrates the accuracy of the proposed design and analysis methodology.

Convergence and Implicit Regularization Properties of Gradient Descent for Deep Residual Networks

We prove linear convergence of gradient descent to a global minimum for the training of deep residual networks with constant layer width and smooth activation function. We further show that the trained weights, as a function of the layer index, admits a scaling limit which is H\"older continuous as the depth of the network tends to infinity. The proofs are based on non-asymptotic estimates of the loss function and of norms of the network weights along the gradient descent path. We illustrate the relevance of our theoretical results to practical settings using detailed numerical experiments on supervised learning problems.

The Polar Coordinate Transformation Numerical Steepest Descent Path Method for Calculating Physical Optical Scattering Field of Quadric Concave or Convex Surfaces

In this letter, the polar coordinate transformation numerical steepest descent path (PCT-NSDP) method is proposed to calculate the physical optics (PO) scattered field from concave or convex quadratic surfaces. In the proposed method, only three triangles integral domains are calculated, which avoids the complicated decomposition in the former NSDP methods. The PCT-NSDP method has a closed-form formula of the contribution of PO stationary phase point. Therefore, the calculation time can be much smaller. Moreover, the workload is frequency-independent. The numerical examples of the radar cross section of a quadratic convex surface demonstrate the high accuracy and efficiency of the PCT-NSDP method.

Precision in high resolution absorption line modelling, analytic Voigt derivatives, and optimization methods

ABSTRACT This paper describes the optimization theory on which vpfit, a non-linear least-squares program for modelling absorption spectra, is based. Particular attention is paid to precision. Voigt function derivatives have previously been calculated using numerical finite difference approximations. We show how these can instead be computed analytically using Taylor series expansions and look-up tables. We introduce a new optimization method for an efficient descent path to the best fit, combining the principles used in both the Gauss–Newton and Levenberg–Marquardt algorithms. A simple practical fix for ill-conditioning is described, a common problem when modelling quasar absorption systems. We also summarize how unbiased modelling depends on using an appropriate information criterion to guard against overfitting or underfitting. The methods and the new implementations introduced in this paper are aimed at optimal usage of future data from facilities such as ESPRESSO/VLT and HIRES/ELT, particularly for the most demanding applications such as searches for space–time variations in fundamental constants and attempts to detect cosmological redshift drift.

On Landmark Distances in Polygons

AbstractWe study the landmark distance function between two points in a simply connected planar polygon. We show that if the polygon vertices are used as landmarks, then the resulting landmark distance function to any given point in the polygon has a maximum principle and also does not contain local minima. The latter implies that a path between any two points in the polygon may be generated by steepest descent on this distance without getting “stuck” at a local minimum. Furthermore, if landmarks are increasingly added along polygon edges, the steepest descent path converges to the minimal geodesic path. Therefore, the landmark distance can be used, on the one hand in robotic navigation for routing autonomous agents along close‐to‐shortest paths and on the other for efficiently computing approximate geodesic distances between any two domain points, a property which may be useful in an extension of our work to surfaces in 3D. In the discrete setting, the steepest descent strategy becomes a greedy routing algorithm along the edges of a triangulation of the interior of the polygon, and our experiments indicate that this discrete landmark routing always delivers (i.e., does not get stuck) on “nice” triangulations.

ANALYSIS OF PARAMETERS OF ROAD TRACKING LIMITATIONS IN TERRITORIAL DESIGN

Due to the need for mass construction of transport routes there is a need to develop theoretical foundations and methods of their design, which will simplify the design process, develop geometric models to optimize transport links, improve existing and create new methods of geometric modeling of optimal trajectories. terrain and road parameters. In the process of designing transport links, the main objective function is the economic effect of their construction. The cost-effectiveness of the overpass should include minimizing the length of the road, taking into account construction costs, which also depend on the minimum allowable parameters of transport routes, the peculiarities of traffic. To develop an optimization model for determining the trajectory of the road in the territorial design, the analysis of geometric parameters of the features of transport routes such as the minimum: turning radius in terms of Rgor; profile angle of rise of the path angle α; profile angle of descent path angle β, profile radius of path convex curves Rprof1; profile radius of the path concave curves Rprof2; step of supporting structures of engineering supports ∆L. And also the maximum height of transport engineering support ∆H. These indicators will serve as limitations in optimizing the trajectory of overpasses. А conditional classification of relief surfaces taking into account geometrical features and parameters of different types of overpasses is offered. Its use will promote increase of quality of designing of transport ways on a terrain relief, simplification of design process and improvement of quality of design planning decisions at territorial designing. The further use of the optimization model to determine the trajectory of roads for different types of transport will improve the quality of design, solving planning problems of spatial design.

Legend descent of Ganga and similarities with impact event

Role of comets and icy asteroids in getting water to Earth is under discussion for last few decades. In the recent history, we have observed and recorded two comet impact events in the solar system. Both the impacts of solwind and Shoemaker levy-9 support the argument that the impacts by comets may be a regular feature and Earth is no exception to it. In the history of mankind, there is a strong possibility that such events were observed by various civilizations.Early settlements of ancient India observed various celestial objects like stars, constellations, planets and comets.Vedas like Rigveda, Atharvaveda refer comets as “Dhumketu”. Certain hymns of Rig Vedastrongly support the possibility of impact event being observed and recorded as eyewitness account. Reference of these celestial bodies is found in various ancient legends of India. These legends may be work of imagination based on real observations. One such legend is descent of Ganga from heaven. As per Valmiki Ramayana many aspects of this legend like its composition, appearance, descent path and effects at the time of descent have close resemblance with the impact event of a celestial body like comet. Ancient Stone carvings depicting the event provide major clue about the celestial movement and the impact event.In this paper we have used ancient description from Ramayana and Veda, and compared it with modern scientific facts and geological features of the region described in the legend.There are Multiple water bodies and lakes in the Tibet behind mount Kailash. This lake region is rich with finds like coesite, stishovite and other ultra high pressure finds that are usually associated with the impact site. These lakes play crucial role in the water cycle of Asia.Though there are lot of similarities in the legend and the available facts, as on date there is no conclusive evidence which can prove the origin of river Gangaas a result of this event as mentioned in thelegend. Thus this legend may be a result of observations mixed with belief.