Residual Part Research Articles

A Cartilage-Saving Technique for Tragus and Antitragus Fabrication in Auricular Reconstruction.

Background: For auricular reconstruction surgery using autologous costal cartilage, younger patients typically have a limited amount of costal cartilage available. Objective: We introduce a cartilage-saving technique for fabricating the tragus and antitragus, and evaluate its effectiveness based on aesthetic score and complications. Methods: For tragus fabrication, the residual part of the seventh costal cartilage was reoriented by 90° to increase its height and carved into a seagull-shaped structure. The antitragus was constructed by bending the antihelix and stabilizing it on the broadened base frame. Postoperative aesthetic outcomes and complications were documented and analyzed. Results: This study included a total of 658 patients with lobule-type microtia, of whom 356 (54.1%) were male and 302 (45.9%) were female. The average age was 6.5 ± 0.7 years, and the average follow-up period was 13.6 ± 3.5 months. The average aesthetic outcome score was 9.0 ± 0.7. Wound dehiscence at the tragus was seen in four patients, while circulation disturbance at the incisura intertragica area was noted in six patients. Conclusions: This cartilage-sparing technique demonstrated effectiveness in shaping aesthetic tragus and antitragus.

FLAIM: A reduced volume ignition model for the compression and thermonuclear burn of spherical fuel capsules

We present the “First Light Advanced Ignition Model” (FLAIM), a reduced model for the implosion, adiabatic compression, volume ignition and thermonuclear burn of a spherical DT fuel capsule utilising a high-Z metal pusher. FLAIM is characterised by a highly modular structure, which makes it an appropriate tool for optimisations, sensitivity analyses and parameter scans. One of the key features of the code is the 1D description of the hydrodynamic operator, which has a minor impact on the computational efficiency, but allows us to gain a major advantage in terms of physical accuracy. We demonstrate that a more accurate treatment of the hydrodynamics plays a primary role in closing most of the gap between a simple model and a general 1D rad-hydro code, and that only a residual part of the discrepancy is attributable to the heat losses. We present a detailed quantitative comparison between FLAIM and 1D rad-hydro simulations, showing good agreement over a large parameter space in terms of temporal profiles of key physical quantities, ignition maps and typical burn metrics.

Separating the predictable part of returns with CNN-GRU-attention from inputs to predict stock returns

The noise and high randomness of the stock market are primary obstacles to profitability. These factors cause stock returns to consist of short-term predictable and stock-specific residual parts. Therefore, it is beneficial to separate and model the two items for forecasting returns in the randomness environment. On this basis, we propose a novel Temporal Return Separation and Restore Forecasting (TRSRF) method. TRSRF first extracts price- and relation-based features from historical stock inputs and uses them to decompose and restore predictable and residual elements of historical returns , respectively. Then it forecasts these components based on historical values. We conducted experiments on the Chinese small and mid-cap, blue-chip, and large-cap indexes over ten years to compare with seven proposed baselines. On the three Chinese indexes our method separately exceeds 6%, 16%, and 22% absolute annualized returns than our baseline. The ablation study also proves the necessity of return decomposition and inter-stock relation modeling. We find that modeling inter-stock relations on small-cap stocks works better than on large-cap stocks. Furthermore, we prove our method might be an implicit ensemble model of the predictable and residual parts, which is why it works stability under various market conditions.

Synthesis process, thermal and electrical behaviors of Ti3C2Tx MXene

AbstractSynthesis of two‐dimensional (2D) titanium carbide (Ti3C2Tx), with the name of MXene, by etching Ti3AlC2 (MAX) for different times 20 (v/v) % hydrofluoric acid (HF) at 40 °C was carried out. The influences of time, temperature and source of MAX on the synthesis of MXene were researched. The MXenes produced were characterized by fourier‐transform ınfrared (FT‐IR) spectroscopy technique, energy dispersive x‐ray spectroscopy (EDX), scanning electron microscopy (SEM), x‐ray diffraction (XRD) and thermogravimetry (TG) instruments. Above 390 °C, MXene layers were considerably oxidizing and forming anatase and rutile phases of TiO2 under air atmosphere. The resistance of MAX and MXene was 3.6 Ω and 116 Ω, respectively. However, the resistance of the residual part of MXene heated to 620 °C considerably increased to 17850 Ω. This behavior is another important piece of evidence showing that the MXene crystal structure has changed significantly and transformed into a new chemical structure containing anatase and rutil titanium oxide (TiO2). The dielectric loss (ϵ’’) and alternating conductivity (δac) of the MAX and MXenes were determined from their impedance measurements. The ϵ’’ and δac values of MXene were compared with those of MAX. Direct curent conductivities of MAX and MXene produced for 24 h were found to be 0.016 S/cm and 0.0023 S/cm, respectively.

Two-stage transfer learning-based nonparametric system identification with Gaussian process regression

Most system identification methods ignore correlations between different identification tasks and do not make full use of historical models when identifying a new process. In this paper, a two-stage transfer learning-based nonparametric system identification method is proposed to improve model accuracy and to reduce identification costs. First, to overcome the transfer capability limitations of the discrete-time model, the target process is modeled as a continuous-time impulse response (IR) function, which consists of a transfer model part and a residual model part, which is regarded as a zero-mean Gaussian process (GP). Then, by utilizing the process geometrical characteristics, the IR functions are classified into three IR domains, and transformation functions within domain or between domains are designed to learn the relationship between the source process model and the target process model. Finally, a two-stage nonparametric identification algorithm based on GP regression is developed: The first stage is performed to select the appropriate type of transformation function through the weighted-derivative dynamical time warping technique, and the second stage is conducted to estimate the transfer model and residual model by using the empirical Bayes approach. Three case studies are conducted to validate the superiority of the proposed identification method.

Additive Manufacturing Process Simulation of Laser Powder Bed Fusion and Benchmarks

As the aerospace industry continues to adopt additively manufactured (AM) parts for flight hardware, process simulation becomes more attractive to improve the manufacturing process by understanding how process parameters affect part quality and performance. Process simulation can also be used to predict and prevent build failures before the printing process. The powder bed fusion process of Ti-6Al-4V material is modeled using commercial finite element software to simulate the selective laser melting process. The thermal history is obtained from transient heat transfer analysis. Both the inherent strain approach and a sequential thermal-mechanical approach are employed to predict residual stress and part distortion. A National Agency for Finite Element Methods and Standards (NAFEMS) benchmark problem is presented as a numerical example. It is a thin wall structure with geometry features that can lead to part defects due to thermal distortion. It is shown that both analysis approaches are able to capture the thin-member bridging behavior, stepping behavior, and general distortion contour plot as those published by NAFEMS.

Use of Submarine Tailings Disposal as Alternative Tailings Management System

The importance of the mining/milling industry in increasing the growth level and welfare of countries is quite high. However, at the end of mining/milling processes, huge amounts of waste (often known as tails) are inevitably produced that have no economic value and can even be considered dangerous due to some heavy metals they contain. These tails are highly problematic due to both their volume (difficult to manage environmentally) and toxicity (potential to cause acid/leach waters) and need to be handled outside of existing disposal methods. This article presents the effective and sustainable handling and application of tails resulting from the enrichment of copper–zinc ores, which are actively engaged in metallic mining activities in the northeast of Türkiye, with the submarine tails disposal (STD) method. In the mining operation under study, some (~55–60 wt.%) of the tails are employed as underground fill, even though the residual part is disposed of by the STD method. The characterization of ore beneficiation tails, their transportation to the subsea via a pipeline system, and discharge monitoring results are detailed in the present investigation. According to the limitations which are indicated by the Turkish Control of Water Contamination regulation, the concentration of Pb-Cu found in the results was under the allowable limit of 0.05 mg/L. The allowed 2 mg/L limit for Zn was not surpassed mainly by the concentration found in the collected samples. pH values were almost above the allowable limit of pH > 5. The results reveal that the STD technique works quite well as an integrated mine tails method in the mine under study.

Mobile traffic prediction with attention-based hybrid deep learning

Mobile data consumption is ever-increasing due to the continuous emergence of bandwidth-hungry mobile applications as well as the drastic increase in number of mobile terminals resulted from the pervasive adoption of Internet of Things. In the 5G+ era, network operators have to deal with new technical challenges on network management, resource optimization and mobility scheduling, which require the ability to perform efficient mobile traffic prediction. Traditional prediction methods using convex optimization, Markov model and linear equations cannot describe the various nonlinearity changes of network traffic. In this paper, we propose a novel traffic prediction algorithm for mobile networks by introducing a hybrid deep learning method equipped with the attention mechanism, which analyzes the traffic in cellular zones to determine the spatiotemporal characteristics in the residential community. The hybrid deep learning model includes autoregressive integrated moving average mode (ARIMA) preprocessing with decomposition ability for time series, external spatial feature variables, sequence-to-sequence (seq2seq; attention-based CNN-LSTM) pretraining and extreme gradient boosting (XGBoost) optimization processing for integrating nonlinear relationships. The CNN method shows good nonlinear generalization ability to mine deep features of community traffic and capture the nonlinear trend. Our proposed approach first decomposes the community traffic data into linear and residual parts through ARIMA and then seizes the deep features of community traffic through the constructed pretraining seq2seq framework. Finally, the pretraining outcomes are further adjusted by the XGBoost method. Simulation results show that the proposed solution improves the accuracy of prediction apparently.

(120) GETTING C-LITERATE: ELUCIDATING BULBOCLITORAL ERECTILE TISSUE ANATOMY AND HISTOLOGY FOR APPLICATIONS IN CANCER SURVIVORSHIP

Abstract Introduction Sexual function is a crucial component of overall well-being and is emerging as an important factor in health outcomes across multiple healthcare fields, including oncology. The bulboclitoris, composed of the clitoris and vestibular bulbs, is an erectile organ that has been largely understudied in comparison to other sexual organs, such as the vagina and penis. Recently, sexual health advocates have increased visibility for the bulboclitoris, highlighting its significance, particularly for patients who have undergone surgical procedures, experienced trauma, or undergone cancer treatments in that region. A deeper understanding of this organ is essential for better appreciation of its role and for advancing the treatment of sexual morbidity. Objective We aim to characterize the anatomic and histopathologic characteristics of the bulboclitoral erectile tissues using human cadaveric specimen dissection, histology, and immunohistochemistry. We hope that our findings can both serve as a translational bridge to understanding the effects of radiation and other oncologic interventions on the bulboclitoris on a cellular level and to establish the bulboclitoris as a unified organ in peer reviewed anatomic literature. Methods We evaluated the bulboclitoral erectile tissues on a structural and cellular level using multiple modalities. In order to visualize the bulboclitoris organ in its anatomic position, we used gross anatomic dissection (n = 2) and cross-sectioning (n = 1). In order to characterize the neurovasculature, endocrine function, musculature, and other cellular characteristics of the erectile tissues, samples were taken from multiple sections of the dissected bulboclitoral organs and from rapid autopsy (n = 2) for histopathological and immunohistochemical staining. We are analyzing these tissues using four stains, hematoxylin and eosin (H&E), trichrome, toluidine blue, and elastin; and eight antibodies, endothelial nitric oxide synthase (eNOS), factor VIII, smooth muscle actin (SMA), desmin, protein gene product 9.5 (PGP 9.5), tyrosine hydroxylase, anti-estrogen receptor (anti-ER), and anti-androgen receptor (anti-AR), using penile tissue as a control. Results We present the results of the gross dissections and some preliminary results of the histopathological and immunohistochemical staining. These dissections confirm the visibility of the bulboclitoris in its specified anatomical location and provide support for the existence of the residual spongy part (RSP) connecting the cavernous and spongy structures. Distinct features of the bulboclitoral erectile tissues are visualized and highlighted on the digitally scanned slides. The results of the histopathological and immunohistochemical analyses will further elucidate the anatomy of the organ. Conclusions The bulboclitoris is an organ that plays an essential role in sexual function. Thus far we have found supportive evidence for the hypothesis that the bulboclitoral erectile tissues function as one organ, homologous to the penile erectile tissues, based on the presence of the residual spongy part (RSP). Greater understanding of the makeup and cellular composition of the erectile tissues has the potential to increase our understanding of various medical treatments on sexual function, provide the basis for objective markers that can help to quantify the impact of any preventive or mitigating interventions, and lay the foundation to inform design of appropriate interventions for the preservation of sexual function in cancer survivorship. Disclosure No.

A nonlinear finite volume element method preserving the discrete maximum principle for heterogeneous anisotropic diffusion equations

In this paper, we propose a new nonlinear conservative and maximum-principle-preserving finite volume element method for heterogeneous anisotropic diffusion equations on triangular or strictly convex quadrilateral meshes. First, we decompose the numerical flux of the standard finite volume element method on each dual edge into two parts: main part having a two-point-flux structure, and residual part owning a multi-point-flux structure. Then, according to the sign of the residual part and the distribution of the local extremum, the residual part is modified to a two-point-flux structure with a nonlinear term. The resulting nonlinear scheme not only inherits conservation and accuracy of original scheme, but also possesses a maximum-preserving structure without extra restrictions on the meshes and diffusion coefficients. Several numerical experiments verify that our nonlinear scheme has an optimal convergence order and satisfies the discrete maximum principle.

A time-frequency-based interval decomposition ensemble method for forecasting gasoil prices under the trend of low-carbon development

Given that gasoil plays a crucial role in carbon emission reduction, in this paper we propose a time-frequency-based interval decomposition ensemble (TFIDE) learning approach to forecast gasoil prices and capture the nonlinear impact of the global trend of low-carbon development on gasoil prices. The proposed method integrates bivariate empirical mode decomposition (BEMD), an interval multilayer perceptron (IMLP) network and a threshold autoregressive interval (TARI) model. First, we use BEMD to decompose interval-valued weekly gasoil prices into a finite number of complex-valued intrinsic mode function (IMF) components and a residual component. Second, we apply the IMLP model to forecast the IMFs and the TARI model to predict the residual part with predictors of carbon reduction technology and carbon emission concerns. After that, we combine all the forecasting results to generate the final gasoil price interval forecasting results. Our empirical results show that our carbon reduction technology variable improves middle-frequency IMF forecasting and that carbon emission concerns have a nonlinear impact on long-term gasoil price intervals. Furthermore, the proposed TFIDE approach outperforms other competing methods under different accuracy measurements.

A New Non-Extensive Equation of State for the Fluid Phases of Argon, Including the Metastable States, from the Melting Line to 2300 K and 50 GPa

A new equation of state for argon was developed with the view of extending the range of validity of the equation of state previously proposed by Tegeler et al. and obtaining a better physical description of the experimental thermodynamic data for the whole fluid region (single-phase, metastable, and saturation states). As proposed by Tegeler et al., this equation is also based on a functional form of the residual part of the reduced Helmholtz free energy. However, in this work, the fundamental equation for Helmholtz free energy was derived from the measured quantities CV(ρ, T) and P(ρ, T). The empirical description of the isochoric heat capacity CV(ρ, T) was based on an original empirical description explicitly containing the metastable states. The thermodynamic properties (internal energy, entropy, and free energy) were then obtained by combining the integration of CV(ρ, T). The arbitrary functions introduced by the integration process were deduced from a comparison between calculated and experimental pressure P(ρ, T) data. The new formulation is valid for the whole fluid region from the melting line to 2300 K and for pressures up to 50 GPa. It also predicts the existence of a maximum of the isochoric heat capacity CV along isochors, as experimentally observed in several other fluids. For many applications, an approximate form of the equation of state for the liquid phase may be sufficient. A Tait–Tammann equation is therefore proposed between the triple-point temperature and 148 K.

Whisker Bond: From Findings to Concept in Refractories

Ceramic bonds are conventionally formed during the<sup> </sup>burning of<sup> </sup>refractory bricks and by using pre-fabricated blocks or monolithic lining, which is characterized as the coalescence of the particles by liquid sintering. However, the whisker bond was discovered with the outstanding performance of unburnt periclase–spinel–Al bricks while substituting magnesia–chrome bricks in the chromium-free campaign of refractory lining of RH degassers. Thanks to the prominent effect of the whisker bond, such a refractory material demonstrates ultrahigh hot strength, high resistance to slag penetration, and thermomechanical stress. Investigations reveal the initial melting of metal Al at the melting point of 660°C, aluminum liquid rims around the cavities formed before ~800°C, gaseous AlN yielded and distributed throughout<sup> </sup>the matrix with increasing temperature, gaseous Mg reduced from ~1000°C, and MgAlON whiskers eventually formed in the matrix. Microstructure observations show a dense interwoven whiskers bonded matrix in most residual parts of the used periclase–spinel–Al bricks. The whisker network in the matrix is made up of<sup> </sup>straight columns<sup> </sup>of 1–5 µm in diameter and 20–40 µm in length, which is different from birdnesting, nano-size curly whiskers observed in the past. The findings suggest a whisker-bond concept in terms of the bond mode of the whisker network and the process of the vapor-solid forming mechanism.

Mechanical property enhancement in additively manufactured NiTi double-asymmetric honeycombs with bioinspired graded design

ABSTRACT The cuttlebone is known for its ability to possess high specific stiffness, progressive failure and lightweight from the porous chambered structure. Inspired by the microstructural characteristics of cuttlebone and incorporating the wall gradient design, a series of double-asymmetric honeycombs were designed and processed by LPBF. Results indicated that bionic structural units with the junction design can maintain the integrity of the residual parts after local buckling and failure, improving the load-bearing capacity. The double-asymmetric honeycomb with gradation parameter α = 2/3 achieved a maximum specific compressive strength of 70.64 MPa cm3/g. As α decreases, there is an increase in specific energy absorption and a narrowing of the hysteresis loop. The as-build honeycomb had undergone stress-induced martensite transformation during compression. The dissipated mechanical energy (ME) decreased with the increasing cycle number and the decreasing α. The results provide design guidelines and process strategies for developing high-performance honeycombs.

Intraoperative selective cerebral angiography for microsurgical treatment of cerebral arteriovenous malformations in a hybrid operating room

Arteriovenous malformations (AVMs) of the brain are a congenital anomaly of the development of cerebral vessels, when instead of a normal capillary bed, a «network» of pathologically altered vessels is formed, through which arterial blood is shunted into the drainage venous system. Due to the thinned wall of the pathological vessels and high pressure in them, patients with AVMs are at risk of intracerebral hemorrhage up to 4 % annually, which determines the vital need for their treatment. Microsurgical removal of brain AVMs is considered the most radical and effective treatment method, the main goal of which is to completely disable the body of the malformation, since the remaining part can lead to the risk of postoperative bleeding. To ensure effective control over the completeness of AVM removal intraoperatively, two methods have been developed: selective cerebral angiography (SCAG) and indocyanine green video angiography (ICG-VA). According to the literature, SCAG provides a number of advantages in the intraoperative diagnosis of residual AVM parts compared to ICG-VA. The article analyzes our own experience in using intraoperative SCAG in the surgical treatment of AVM in a hybrid operating room and examines the literature data on the topic of the paper. Our study highlights the importance of using the method of intraoperative control through SCAG in order to improve the effectiveness of surgical treatment of cerebral AVMs.

Surgical treatment of intracranial epithelioid hemangioendothelioma: a case report

Epithelioid hemangioendothelioma (EHE) is an extremely rare vascular neoplasm with an intermediate pattern of malignancy between benign neoplasms and angiosarcomas. Only 46 cases of intracranial localization of primary EHE in adults have been published.Case report: A 47-year-old male patient developed pronounced speech disorder of sensory and amnestic aphasia type, right-sided pyramidal hemiparesis within 3–4 days. Magnetic resonance imaging revealed a delimited left sided brain islet neoplasm with signs of hemorrhage and small perifocal edema. Intraoperatively, the neoplasm was represented by a conglomerate of pathologic vessels, with involvement of the terminal branches of the M2 segment of the middle cerebral artery, which prevented radical resection of the neoplasm. Based on histopathological and immunohistochemistry analysis of the neoplasm (positive expression of CD31, CD34, proliferative activity index Ki-67 10%) the morphologic diagnosis of EHE was established. 3 months after surgery, continued growth of the residual part of the neoplasm was noted. Temozolomide chemotherapy was clinically ineffective. The patient died due to the development of dislocation syndrome after 9 months.Discussion. The malignant characteristics of EHE include invasive growth, recurrence, and metastasis, which is more common in intracranial localization of the neoplasm. If EHE is suspected, radical surgical removal of the neoplasm should be sought.

Simultaneously manipulating carbon coating layers and void structures in silicon/carbon anode materials via bifunctional templates for lithium-ion batteries

The carbon coating strategies, ameliorating structure instability and reaction kinetics of silicon anodes upon lithiation/delithiation, have been chronically plagued by an electrochemical contradiction between a high specific capacity from a high silicon content and a long cycle life from a high carbon content. Herein, the carbon coating layers and void structures for silicon/carbon composites were simultaneously manipulated through a precisely grown Al2O3 template, which induced a controllable polydopamine polymerization through its mild interfacial interaction with Tris-buffer solution and created abundant void spaces by its residual parts. Particularly, the as-optimized silicon/carbon composite with an ultrahigh silicon content of 89.3 wt% could demonstrate a large initial reversible capacity of 2583 mAh g−1 with an 82.1 % coulombic efficiency at 200 mA g−1, a remarkable cycling durability of 601 mAh g−1 after 990 cycles at 2000 mA g−1, and an excellent rate capability of 887 mAh g−1 at 4000 mA g−1. The uniform void structures could maintain the structural stability/integrity of silicon, boost reaction kinetics across electrode/electrolyte interfaces, and suppress the uncontrollable formation/evolution of solid electrolyte interphases upon cycling. This novel research on synchronously regulating carbon layers and void structures in silicon/carbon composites would enlighten a rational development of high-capacity and long-life silicon anodes.

Principles of management of patients with short bowel syndrome

Short bowel syndrome (SBS) is a rare disease accompanied by the phenomena of malabsorption (impaired absorption of food) and maldigestion (phenomena of creato-, steato-and amilorrhea), as a result of resection of most of the small intestine (usually with a residual part of the intestine less than 200 cm) from – due to various etiological factors. One of the severe complications of this syndrome is the development of intestinal failure, which can be manifested by the occurrence of water, electrolyte and white matter disturbances, hypovitaminosis, and deficiency of micro-and macronutrients. It is possible to suspect the development of intestinal failure if the patient continues to have repeated diarrhea 2–3 months after surgery and a progressive decrease in body weight by 5% or more of the initial weight within a month. Therefore, an important aspect in the treatment of SBS is the correction of electrolyte disturbances and maintenance of nutritional status. However, the severity of the patient’s condition is often determined not only by the course of the disease itself, but also by the long-term use of parenteral nutrition after surgery. Therefore, an important aspect in the management of patients with SBS is the cessation of parenteral nutrition as early as possible and the transition to a physiological nature of food intake. This can be achieved both by choosing certain surgical treatment techniques and by using drug therapy – an analogue of glucagon-like peptide-2 – Teduglutide, which increases the functional ability of enterocytes to absorb. SBS is a significant social problem due to the high mortality rate in childhood and a significant percentage of disability in people of working age, which makes it highly relevant to discuss the management strategy for this category of patients.

Innovative joining technologies for lightweight material vehicles

The transport industry is one of the most important for society and its economic growth. In Europe, this is especially true for road transport, which is an essential pillar for employment, trade, and economic development. The challenge is to minimize energy and cost and maximize efficiency while ensuring comfort and safety. This is the driving force behind technological progress that with social changes (such as, changing consumer preferences, greater environmental awareness) and political changes is revolutionizing the way people and goods move. Nevertheless, the selection of lightweight materials is negligible; it could involve new manufacturing technologies and joining techniques. Jaguar Land Rover (JLR) has been one of the prominent car producers employing aluminum alloys since 2003. A typical JLR monocoque is characterized by 90% aluminum stampings components made of 5xxx and 6xxx series aluminum alloys. Audi Space Frame (ASF) represents an alternative interpretation of improved lightweight frame architecture, and it is characterized by aluminum for more than 80% with the residual parts in CFRP used for rear panels, tunnel and the components useful to higher torsional stiffness. A 30% weight decrease is reached with respect to traditional steel corresponding elements. This review shows an overview of the challenges and opportunities for automotive body structures in the coming years while maintaining the goal of reducing mass and improving sustainability without increasing costs and impacting safety. This manuscript first evaluates how we can reduce mass in vehicles minimizing the carbon footprint and developing recyclable structures. The potential of new materials will be shown in light of the design constraints and the choice of technology used. The final remarks will discuss opportunities for engineering innovation dictated by this period of great changes and needs.

Gaussian process model based restoration of damaged Buddha statue head

Buddha statues are distributed worldwide, and each piece reflects the aesthetic fashion of a particular region and historical era. Therefore, these sculptures have important cultural, aesthetic, and historical value. Owing to natural or artificial destruction, several Buddha statues have been damaged, with head or facial damage being the most prominent damage type. Because Buddha statue heads exhibit intricate variations in facial expressions and proportions, restoring head or facial damage is the most challenging aspect of damaged sculpture restoration projects. This study provides a new method for the restoration of damaged statues based on a Gaussian process model. The Gaussian process model entails a type of statistical shape modeling that allows it to learn shape distribution properties from a training dataset. During the restoration process, we used the residual parts of the damaged shape for the observations and added them to a Bayesian inference system to obtain the possible restoration result in the form of a posterior distribution. Therefore, the proposed method can be regarded as a quantitative mathematical representation of the subjective deduction process. Compared to those of the traditional manual restoration method, our results were more repeatable and stable, and the restoration process was automatic and rigorous, which reduced the requirements for professional knowledge and experience. Based on the learned model information, the proposed method exhibits strong robustness and anti-noise properties. In contrast to the optimization method, our final restoration result is a probability distribution, applicable to the repair of cultural relics. As our method make the missing shape inference using residual shape information and the regularity learned from training dataset, it is suitable for the restoration of damaged parts with no direct shape evidence. Finally, our model is generative; in other words, we can generate shapes on the posterior distribution and provide the corresponding probability. To demonstrate the effectiveness of our method, a series of experiments were conducted to restore damaged parts under different parameters and damage type settings. Subsequently, a quantitative analysis was performed. Finally, we applied this method to the virtual restoration of a damaged Buddha statue head in Xi 'an Museum.